Your guess: construction start/end dates for MEA Arks?

Bryson was already studying legends of the Reapers ... as well as Reaper-killers. So the idea existed there might be a threat to galactic civilization out there ... credibility and more solid proof was what they lacked. Shepard would eventually provide proof, even if it seemed the information was not appreciated by the major Citadel races.

Ark ship technology, primarily their propulsion system, was based on the technological concepts gleaned from the Prothean beacon on Mars (and maybe the beacon on Thessia), for creating long-range, long duration FTL travel. Early on, it would have just been concept development, technology development ... to help go places in the MWG that lacked Mass Relays.  Then as the technology started to bear fruit, the idea of going beyond the MWG was raised, combined with more evidence of Reapers. So the technological focus switched from intra-galactic travel without use of Mass Relays ... to intergalactic travel. A lot had to change. Stasis chambers for the organics. VIs to run things for extended periods while the crew "slept" during the long journey. Ability of the Ark ships to become "live ships" once the travel between galaxies was over and exploration of the new galaxy had begun.

Then the building. Would take a long time for just one species ... given other demands on a species' resources ... at best, Turians, Salarian, Asari and Humans species would probably only be able to build a couple of Ark ships apiece. It would be beyond the resources of the Krogan, Hanar, Quarian, Elcor and Batarian races ... also, Batarians and Krogans would fail the trust factor with the advanced technology. The Volus might team up with the Elcor. You would probably have a few contractors ... rather than each species gearing up for the manufacture, you'd see it broken down into component pieces and assembled elsewhere. That could speed the construction process and alleviate some of the learning curve issues if each species was not expected to develop a "soup-to-nuts" Ark ship manufacturing process on their own. Some Quarians might be brought in, for their expertise in "live ships" and long duration space travel - applicable to once they get to Andromeda, not so much use with respect to the intergalactic portion of the mission, but it would effect ship design significantly.

Maybe why it was not discussed in a big way in MET, the original concepts looked at intra-galactic travel, without use of Mass Relays. It didn't become apparent, until later, that intergalactic travel might be necessary, then, because of concerns about indoctrination, the work was "hidden in plain sight."  Just as the Prothean beacon on Thessia had been hidden by the Asari, the Alliance and major Citadel races hid ARKCON by saying they were building intra-galaxy exploration vessels ... when in fact they were building Ark ships capable of intergalactic travel.

The Illusive Man was wrong, the Alliance wasn't wasting time, but they were looking for something different in data recovered from the beacon in the early years, rather than what Cerberus was looking for, circa Arrival/beginning of ME3.  When the Reapers were known to be months ... or at most a year ... from Earth, priorities of the Alliance changed, more resources were placed on analyzing other elements of the Mars data ... and the plans for the Crucible were found.  But this was after completion of the Ark ships ... probably about the time of their departure ... a few months after Arrival.  Unfortunately for the humans, they only had a few decades to study the Mars Beacon, not the millennia that the Asari had to benefit from the Prothean beacon on Thessia.  So potential advances and technological breakthroughs were limited.