Hermione met Harry and Ron in their compartment on the Hogwarts Express, but that doesn't mean they hadn't noticed each other before then.
Hermione stood by her parents as the three of them stared openmouthed at everything around them. Owls hooted, older students carried brooms and discussed Quidditch tactics, and wizards and witches kept appearing through the archway she herself had entered half an hour earlier, wanting to be on time. The general hubbub was exciting and trepidatious at the same time.
She had of course been very surprised when she received her Hogwarts letter, but after the wizard assigned to explain the wizarding world to her had finished describing Hogwarts School of Withcraft and Wizardry she had immediately become enthusiastic about her new school. She must have read her new copy of Hogwarts: A History four times already. Here was her chance to really belong. At the age of eleven, she wasn't like the other children at her school. They wanted to play at recess while she preferred to read, they liked arts and crafts whereas she didn't understand why they were wasting time on a subject that clearly wasn't on any exam they would ever take, and while they played sports on the weekend she went to the library. She didn't have many friends. Her peers were always friendly to Hermione, but she just never seemed to really click with any of them. She had her parents, of course, and now she had a whole new world in which to find friends who shared her love of learning.
She watched the families surrounding hers with particular interest. She slightly envied those students with siblings having grown up an only child herself. One such large family stood some 20 feet away from hers and she initially took notice of them because they all had bright red hair-the parents, the older, smug looking boy, the identical twins, the little girl, and the boy who looked slightly ill as his mother rubbed at his nose with her handkerchief. Maybe he was a first year as well, she thought. He looked about the same age as her and perhaps his wan face was the product of the same sickly anxiety that she was now feeling. She watched them for a minute more as the older boys flitted away, no doubt in search of their own friends, and the little girl pouted as what looked like final goodbyes were exchanged.
Ron said a quick goodbye to his parents, or as quick as an unrelenquishing Molly Weasley would allow, and boarded the Hogwarts Express for the first time. He couldn't wait to get to school, but at the same time he was afraid of not living up to his brothers. Bill had been Head Boy and really cool, Charlie was captain of the Quidditch team and worked with dragons for God's sake, Percy was a bit of a tosser but he was smart, Fred and George were true pranksters and very popular, and Ron? he was a lanky, awkward eleven year old boy with no standout qualities. He tried not to dwell on this as he walked through the hallway finding compartment after compartment full of reunited friends. Forced to stop outside of a particularly ruckus-like compartment, in which he managed to peak a glance of the twins entertaining a crowd, Ron glanced out the window onto the platform. Only straggling students and a handful of parents remained and as he waved to his mum, dad, and Ginny he caught a glimpse of another small group. Two people who were clearly Muggles, he noticed by their lack of robes and obvious understanding of Muggle clothing, were giving goodbye hugs to a rather bushy-haired girl. She wasn't weeping; however, he thought she looked excited and determined. He couldn't imagine what it was like for a Muggleborn coming to Hogwarts for the first time. It was a scary enough adventure for him and he was the sixth kid in his family to attend. He watched the girl as she walked towards the train with slightly clenched fists. What could she be thinking, he wondered. He was jostled from behind and in the second it took him to turn and make an apologetic gesture at the boy behind him he lost sight of the girl. He looked around the platform once more, but assuming she had boarded the train he continued on until he found the compartment where the black haired boy he had met earlier sat. He slid the door open and asked if he could join him as everywhere else was full and took his seat.