If we can get there, nearly a billion years of cycles could have gotten there, too.
No, there's a couple of crucial differences between our cycle and every other cycle.
Firstly, the Protheans changed the Keepers' signalling so that they wouldn't open the Citadel relay and let the Reapers in for a surprise attack. In every other cycle the Reapers took control of galactic transportation and communication on day one of the war, wiped out the galactic leadership and seized control of all the records on the Citadel. I think it would be exceedingly difficult to coordinate an ark project without the ability to transfer people and materials across the galaxy quickly. Vigil in ME1 says in the Protheans' cycle, individual star systems were cut off from one another. It's actually kinda a miracle that so many of the cycles were able to start work on the Crucible, given how dispersed their resources and militaries would've been.
The other thing is that our cycle was the first time that the galaxy killed the Reapers' vanguard and had advance warning of the Reapers as a galactic threat to all life that would not accept surrender. We had knowledge and time that none of the others had.
Remember that when every other cycle was confronted with the Reapers (in their individual systems, because their leadership was already dead) they had no idea what the Reapers wanted or where the war would end. Why would anybody plan for an idea as far-fetched as leaving the galaxy if the easier solution was to run and hide within the Milky Way? 99% of it was totally unexplored, as people keep screaming about here.
An ark to Andromeda requires an understanding that *nowhere* in the Milky Way was safe from the Reapers, that they would never stop until all advanced life was exterminated, and that there was no possibility of surrender or waiting them out. Nobody else knew that, except the current cycle - and even if they did, they would've had no time to prepare before being invaded en masse. We understood - from the Protheans - that the only way to escape the Reapers with any degree of certainty would be to leave the galaxy entirely.