Her parents were orthodontists. They worked, somewhat, under the purview of the NHS, and thus, got some of their funding from that entity. That gave them, as she was aware, some contacts within that group that went beyond what a normal person would have. Nothing like a cabal of medical professionals or the like, just the knowledge of what hospitals were better stocked than others, and where doctors were more likely to have specific skills.
As such, they knew people that would love to get their hands on things like a blood replenishment potion, a scar healing salve, or the various poultices for wounds and the like. She even showed off some of the things her parents might not like, for the fixing of teeth and such, though, surprisingly, they were thrilled that the magical world had specific dental care potions, as it showed they recognized it was a unique medical science, which took muggles quite a while.
Potions for regrowing bones, things to 'quiet' the mind, for things like PTSD. Painkiller potions were the ones they were, strangely, the most excited about, as those without side effects could really revolutionize some forms of surgery, especially if they allowed them to do so without needles, as people were far more likely to drink something than to let you stick a big needle into their jaw.
After discussing all the possibilities, they sorted the potions out, labelling them as they went with their effects, coming up with names that sounded like medical terms, if you were unfamiliar, but were, in fact, gibberish of the highest order. They began to talk between themselves about which ones would do the most good where, and what places would pay the most, with her mum reminding her dad about some people in the States who would pay an arm and a leg for some of these.
The next day, as they went off to work, she took the bus to her local library, and made a show of grabbing a few textbooks that were suitable for her age group, while moving down the stacks in a few places to use her spell. It took effort, as she forewent the use of her wand, which she was now certain was the thing used to track underaged magic. This was proven if not true, then at least weighted in favor of it as seven casts of her spell did not cause a single scrap of robes to suddenly appear and grab her, and no letter materialized out of the air to inform her of her transgression.
Still, seven was her limit, she could feel it, as without her wand, her spell was simply not as efficient. It galled her to think that she would be back to such a small number, especially given the library here had so much more and varied knowledge to be stolen, but she let it hang, and after a few days she had gotten good enough with her spell wandlessly to more than double that number, which was better than nothing.
It took most of June for her parents to finally start being able to pass off her potions, but once they did, the orders for more came in almost immediately. Mind, they were still selling them 'on the sly' as the saying went, her mum setting up a shell company, something she refused to explain how she knew how to do to either her husband or her daughter, but even doing it one vial at a time was proving profitable.
By the end of the month, they had started to turn a profit quite handily, and so her plans were put into motion. She ordered first a piece of silver spun cloth, expensive, but worth it as she found it was exactly as conductive to her magical energy as she thought, acting as a multiplier for her power…though equally destabilizing any spell she tried to cast through the thing in the park.
Worse, and one of the reasons she'd picked a private corner of a public area, it seemed that bigger exertions of magic COULD be detected, as her third spell saw someone in very odd looking dress, obviously trying not to stand out, and doing quite the opposite, simply appearing out of thin air. Quickly, she pocketed the piece of cloth, and waited as the person, very unsubtly, pulled a wand from their sleeve, and began to investigate.
They found nothing, obviously. Hermione had used an extremely subtle form of the 'Notice-Me-Not' spell on herself, so even as the person, a woman of middling years, looked right at her, she seemed to find nothing. Grousing how 'Bone had sent her on another bum assignment', she then just vanished, in full sight of a few of the park's open areas too, showing how little the woman cared about being spotted…or more likely how little respect she had for non-magicals.
Regardless, Hermione continued to test her silver cloth, eventually discovering that it amplified magic passing through it, but that she, if she wore it, could keep the magic's 'shape' as she wanted it for her spells. This led to a few wonderful weeks of testing, before finally, she and her father working together were able to sew together a fingerless glove for her to wear, one that seemed to amplify her power many fold, while maximizing her control.
As she fashioned her glove, her mum again had to voice the question of why no wizard had ever figured out this simple trick, but Hermione, having gone over her knowledge, had realized why. The silver made it harder to cast spells, and until recently, there were so few wizards in the world spells were 'coarser' and required more focus to cast, so any disruption in them was seen as a bad thing.
They were figuring it out, slowly, as she began to peruse her wizarding law books up to today. Cauldrons were being made with new metals, purer ones, and the weight of coins was changing. Everything spoke of a society slowly noticing this thing under their nose, but it was also still out of reach, as none of them had made the leap to figure it all out the way she had, as they simply didn't understand things like electrical current, resistance, or capacitors.
Her father helpfully supplied that any children her age not quite as smart as her would have heard of those things, but would be overawed by the magical world enough to forget such mundane affairs, and never think of it in detail. Hermione's education led her down tracts that the average magical wouldn't or couldn't follow, meanwhile the Purebloods simply ignored out of spite.
With her glove made, she set about testing other ideas. Fabric, as she had found, was too unwieldy, causing too much disruption, but a quick test showed that runes forged in silver did well, so after acquiring more silver thread she set about testing things, sewing single runes into basic pieces of cloth and then channeling a small amount of magic into them, being excited as the runes lit, and then testing them on their potency.
The warmth rune actually caught fire, the chilling one caused frost to form, and she even had her father take her to a place he knew where they tested firearms. A quick bribe and they were able to supply their own target, the specially treated fabric managing to take several direct hits before finally breaking, with her excited to see the specifics of how the three test cloths broke so she could layer them properly over each other.
Finally, she began to work on her school robes. They had many basic enchantments on them. Self-cleaning and self-repairing, because otherwise the school, even with those disgusting leeches to help, would have trouble affording their maintenance for several hundred students at a time. She sneered remembering those things in the castle, but put them and their history out of her mind as she worked more.
At the end of July, as August reared its humid head, she was almost finished with all three sets, with various runes sewn into them, hidden between layers so as not to arouse suspicion as she made use of their power. That had taken some time to get right on its own, and she'd even had to 'waste' several of her books a day on some sewing techniques before they got it right on three chosen robes.
The first was for boosting the strength of her spells directly. The rune arrays did that simply and effectively, being words that directly correlated to that basic idea. She even got to see several more auror agents, most of which were just as bad at being inconspicuous as the first as she tested her design out, blowing away rocks quite pointedly with a dozen different simple spells cast wandlessly, using fire, electricity, and even one that was purely force in the form of a bolt of colored light.
Once she was done with that fun, she focused on the opposite, doing her best to look through her memory, and several books she'd bought for the purpose of studying them without using her spell, she found every defensive rune she could, and then took the time to slowly whittle them down, weaving together the best she could and finally putting them into practice.
Strangely, where the power boosting runes, because of their mutability, could be combined together easily, the defensive ones, being designed against specific elements, refused to coalesce in quite the same way. Still, after a dozen failed attempts, she had a robe that, the moment she channeled even the slightest bit of magic into it, became armor for all intents and purposes, while still functioning as a garment.
Excitedly, she then got to work on the optimum way to combine the two forms together. She had thought, perhaps, of simply making a double layer, but her work on the defensive robes had shown her why that wouldn't work, especially that one time she layered too many on top of each other and the thing froze solid, proving strong enough that her father had to use, and ruin, some of his dental equipment to break the rune chain to get her out.
Still, lessons learned, she knew what trade offs were needed now, and with only four failed projects, none of which exploded this time, she had worked out a set of robes, self adjusting so she'd never need another, that could not only boost her spell power by a dozen or more fold, but could instantly create an invisible field around her, protecting her from danger. She even included a predictive rune, from divination, as well as one that would slow her down in the event of a protracted fall, just in case.
Testing it proved its potency, though this time the aurors apparently either didn't sense her, or simply decided to stay away, allowing her to experiment in peace as she lifted one boulder atop another, made a tree turn upside down, and finally blew a wind into the sky powerful enough to move some clouds from the ground, showing focus, power, and still allowing her to take a hit when she used a charm that fired another bolt of light, that then spun around and hit her instead of going straight.
Despite the boost to the charm, which was a low tuned stunner, she barely felt it, and smiled to herself, having mastered…okay not mastered but at least gotten a basic handle on wandless magic over the course of her studies in a month and some extra. Some of that was thanks to the various tomes she'd absorbed, but she knew more than a slight amount was she had the talent to use that knowledge well, and she intended to.
Smiling to herself on that first week of August, her school's first day back looming, Hermione Granger, whose name would eventually echo in all the halls of power in the Magical World, snapped her fingers. On cue, a tiny bit of flame danced between her fingers, as she wrote her name with it in the air before her, showing to herself that even boosted, she had kept her control. One man, walking a path in a wooded area, would remark to his family on hearing a disturbing laugh on his jog, but it would be forgotten by all of them in a day, despite all it portended.