Depends heavily upon what aspects of the setting you are changing.
According to
the timeline the first Luna colony was established 2069 on the 100th anniversary of Apollo 11 and the first Martian colony on 2103. Eezo was discovered 2148 and the Charon Relay 2149. Humanity's first extra-solar colonies were established starting 2152. The First Contact War occurred in 2157. It is currently 2174.
Following this timeline humanity's extra-solar colonies contribute basically nothing to our population because they've only been existence for a single generation. So all our population growth has to have taken place within Sol.
Current projections from the UN suggests that human population will peak around 2100 at 10.9 billion and basically zero growth. Honestly that is probably a fairly reasonable value for Mass Effect and in line with the
canonical Earth population (11.4 billion) considering that Earth is suffering notable climate damage including oceans raising 2m and frequent violent weather effects. The other colonies in the Sol system don't really contribute much canonically as I
outline here with the total Sol population only increasing over Earth's by 8 million which is reasonable enough considering Luna and Mars (93% of the non-Earth population) are basically uninhabitable outside (expensive) arcologies. Overall I don't really think the numbers given in Mass Effect for population are really that unreasonable for a civilization that only left its home system a generation ago.
However for the sake of argument lets consider something of a best case scenario. The highest growth rate shown by the UN projections (Constant-fertility) puts us at 21.6 billion by 2100 with a growth rate of 2.114% per year. Continuing that projection out to 2175 gives 103.7 billion people. That does make humanity more competitive on the galactic scale although still well behind even unreasonably low projections of the other species* out there.
*Take the Turians for example. Lets imagine that the Krogan Rebellions, the last major galactic conflict, were unbelievable (as in literally unbelievable) and reduced a millennia old space fairing civilization to just 10 billion people. Lets further say that despite being quite similar to humans they only averaged a 0.5% year on year population growth in the 1,375 years since the Krogan Rebellions ended. That alone is enough to bring them up to 9.5 trillion. Even if we assume they are limited by available territory, which would be odd but okay, they have at least 18 systems (Palavain + 17 Turian Unification War colonies) and from the earlier human projects we are assuming a single solar system can support at least 60 billion so that alone should be 1 trillion or ten times the
best case scenario for human population.
Now you could make some fairly significant changes here by adjusting the timeline of human expansion. However that runs into serious issues. For example if you say we started opening Relays back in 2100 that would give four generations of colony populations which while still low would help bump up human populations. However that requires either pushing back the First Contact war ~50 years or somehow justifying how humanity, which was rapidly expansionistic at the time, didn't run into aliens for 57 years of opening every Relay they could find.
Honestly a lot of the claims about humanity, and a fair number of its feats, in canon would be a lot more reasonable if the timeline was more spread out. As I've
mentioned previously a fair number of canonical characters should actually remember the discovery of Eezo. In fact considering Revy was born 2154 while Eezo was discovered 2148 (6 years prior) Revy's
parents should remember a time before Eezo. If you spaced things so that humanity discovered Eezo in 2148, spent the next century colonizing the neighborhood with FTL ships, discovered their first Relay (which for this probably wouldn't have been Charon) and increased Relay distances such that they spent decades expanding before running into the Turians that would probably make things more reasonable. A 24th century Mass Effect humanity would have first wave colonies with ~150+ years of growth and development behind them creating a strong core followed up by post-Relay colonies with two or three generations creating a vulnerable but valuable outer regions that we've be conflicting with the Batarians over.
Prometheus is the same just remove all the armor and anything else that is military related.The Atlas Titan is the first Titan produced by Paragon industrious for military use, it comes in at around 5.4 meters tall. And is powered by 20 Paragon industrious Arc reactors.
