Liara hints at this nicely in ME1 when you talk to her and she offers a possible reason for why humans appear to be developing so fast. You discuss it with her when she talks about finding it difficult to speak to humans, and she tells you that many of the other species find humans intimidating because they're so goal driven and in a state of rush: both Shepard and her offer the reason that it's because our lives are so short relative to the other sentient species.
Because we live such short lives we want to accomplish something within that relatively short amount of time, making us progress at a fast rate. In addition, we also have a high reproduction rate to account for those short lives resulting in a high amount of diversification, population increase and arguably evolution. As an example through parallel, take Liara again as an example: she appears to be the only child of Benezia, an Asari who has lived most of her life so is probably around 800-900 years old. Think about if that were an 800-900 human...she probably would've had 20 children by that age!
The other species generally seem to be calmer and more 'settled', meaning their progression is more linear whereas ours is almost exponential. Our rate of advancement is high but we also reproduce quickly which just adds to that already high rate of advancement - we operate in a state of rush...this is probably what allows us to outrace them.
What's ironic is that, at least in terms of augmentation, general technology and our own abilities, I expect that in reality we'll actually be further advanced as a species by 2148 than humans are in Mass Effect. I say 'general technology' because I omit Mass Effect-like technology from that opinion