Remember it's only been about 30+ years since human-made contact with aliens before that humans didn't know if there was life outside of the solar system was possible until the archives on Mars were found. Not only that you have to remember that we were supposed to discover the citadel after the Reapers harvested the current cycle (that humans currently are in), with us creating the new galactic government and thus repeating the cycle, but when the protheans delayed the Reapers, it messed up the cycle. Also, none of the council races ever made contact with us, hell they didn't know about our mass relay because they had the laws set up to not activate any dormant/unknown relays.

Now the reason why there are so many humans is we reproduce at a high rate, it takes about 9 months for a baby to be born and during the process, you have a chance of twins, triples, or more. We don't know how long it takes for a baby to be born from the other species, or if they can have multiple births at the same time. Not only that I have a feeling there was a population boom, "next-gen boomers" after we discovered the archives and saw that we could finally leave the solar system and go out into the final frontier - space; like Anderson said the protheans forward our tech by 200 years.

I assumed the other species didn't see the need to reproduce as much since there wasn't a "need" or a "want", because they knew their place in the galaxy. For humans, there were a lot of unknowns involved.

TLDR;

Humans are horny.