To understand the galaxy humanity arrived in during first contact, one must first look at the 5th Golden Age that came before it and the galaxy left in the wake of its fall.
During the early 21th century, after the galaxy recovered from the loss of the Quarians and the Geth War, the 5th Golden Age began. This age was marked by an extreme level of both economic growth and expansion into the Terminus Systems. Colonies from all races across Citadel space were formed even into the farthest depths of the Terminus System, filling the already burning fires of the economic boom.
The Golden Age continued for over a century, a period of great prosperity for the Citadel Races. That was until the early 2130s, when the cracks started to show. The defenses and economies of the Citadel Races were overstretched due to an extreme increase in the rate of colonization in the early 22nd century. This increased rate of colonization also led to heightened tensions with the powers of the Terminus Systems, already unhappy with the colonization of the Golden Age.
This all led to the 3rd Terminus Crusade, where a significant amount of the Terminus Powers joined forces and attacked Citadel space. The Crusade lasted four years between 2131 and 2135, and caused massive amounts of damage. The greater harm, however, was done by the great economic panic caused by the Crusade. The stock market went into freefall, many colonies were almost entirely abandoned by their backers in Citadel space, leaving the colonists on their own deep within the Terminus Systems, debt and bankruptcy rose sharply not only among companies but also governments, with several small races and an entire Salarian Dutchy declaring bankruptcy, with the Hierarchy almost following.
The Crusade and the economic crisis led to the Citadel Races' militaries being stretched even thinner than before, especially the Hierarchy. The Hierarchy was forced to strip the defenses of the Citadel-Traverse Border almost bare to contain the Crusaders on the other side of Citadel space. This proved almost fatal to the Hierarchy as a Terminus raiding fleet crossed the Traverse to strike at the newly developed colonies while they were undefended.
The "March to Gothoine" (named for the colony where the fleet was eventually stopped) devastated the freshly built Traverse colonies, leading to the near abandonment of the area by the Council. The greatest strike by this was the Hierarchy, which was the greatest investor into the area.
By the time things began to stabilize in the mid 2130s, the economy was in ruins and the ability of the Citadel Races to defend their territories was in question, a doubt that only emboldened pirates and other criminal elements into action. Even 20 years later, the galaxy remains in a low level depression, unrecovered from a blow taken in only half a decade. Militaries are stretched thin defending the vast swaths of territory held by the Citadel Races, and though the situation is getting better, full recovery seems far away.
Each of the Council Races were hit hard in one way or another: the Salarians were some of the largest investors into Terminus colonization, leading to great losses when they proved infeasible. The Asari, while not as invested in colonization, were harmed most by the Crusade, which struck many Asari worlds and important trade partners. The Hierarchy was hit the hardest, with its fleet spread thin and many of its new colonies in ruin, the Hierarchy lacked the ability to patrol all of Citadel space. The Hierarchy tried to get more support from other races, but the economic troubles across Citadel space made any military buildup unpopular to the populace of most races.
This is supposed to explain why the Hierarchy was a bit trigger happy during the First Contact War (their new colonies in what would later be known as Systems Alliance Space were devastated in the area), why there is little colonization in the area later controlled by the Alliance (most colonization was focused on the Terminus due to existing infrastructure, being better explored and having more accessible Relays alongside those that existed being crippled or wiped off the may), how humanity grew so fast (the Alliance was fresh and in an economic boom while the galaxy was in a depression, it also explains some of the dislike for humanity, they are prospering while the rest of Citadel space is still recovering) why there are lots of Citadel Race colonies across the Terminus Systems (they were built in the Golden Age when the Citadel Races were expanding into the Terminus), and why the Council is so concerned about aggravating the Terminus Systems (they were left in ruins by them only half a century before).
[Too rambling, plan to split up into two or three different entries]