So I posted my own theory in a new thread because I didn't see this one. I haven't seen this idea floated here (I promise I searched) so I'll post it here where people are interested in this question and can discuss my hypothesis's merits (or lack of them) if they want too.
As I see it, getting to Andromeda is only half the issue. The Disk of Andromeda (~220 ly across) is as much twice the diameter of the Milky Way (100-180ly), so it has approximately 4 times the area. It has roughly the same mass, so there would be approximately the same number of stars, but they would be spread out thinner. It is possible, given the error bars on the numbers involved, the density may be similar, or possibly higher.
A lot of people in this thread seem to agree that mass relays in Andromeda are unlikely. Without relays, exploring even a small portion of Andromeda would take decades, assuming you didn't ever return to some sort of home base. Previous Mass Effect games have taken place in the time span of a few months each. Even assuming a huge improvement on current mass effect drives, it would still be several years to get from one side of the galaxy to the other, without detouring around the center. This seems impractical both from a "realistic" standpoint and from the perspective of game play.
Instead, I propose something else. There seems to be a taboo of studying the Citadel and Relays, which I think might be a very very subtle indoctrination, which could be broken or turned off in the endings. If the secret of the advanced FTL the relays use was discovered, it could be harnessed to build new relays. Everyone, in universe and out, assumes there needs to be a "transmitting" and "receiving" relay for the FTL to work, but we don't *know* that. The reapers don't seem to be very innovative, and the point to point network is perfect for their plan, no one will go off the rails. So, hypothetically, a "Mass Effect Relay Drive" could be a possibility, enabling the FTL speeds of the relays, without requiring a pre-existing relay network . Developing this would of course likely take at least a few decades, possibly a century or more. This would enable not only a much more reasonable trip to Andromeda, but also allow rapid movement within Andromeda itself. In fact, this could even permit return trips to the Milky Way.
I also would like to point out that Matriarch Aethyta proposed studying the Relays and even building new ones. She also hinted Benezia was in agreement on the what, if not the how of this. Liara might decide to use here influence and resources as Shadow Broker to carry the torch of this research in her parent's memory. So if the scenario I'm proposing is correct, I think there is a decent chance Liara may show up, at least in the backstory. As a Liara fan, this makes me happy.
A lot of people are suggest that the humans+ other Milky Way species left before ME3 on a stasis/generational ship. I like this because it sidesteps the endings and their consequences on the future. This may very well be correct, but still, it also means that a lot of Sheppard's story is no longer important, and also feels like a something of a cop out. Additionally, this does not help with my first point about travel within Andromeda.