It has nothing to do with preferred endings its to do with consistency and believability, there is no way that intergalactic travel can be developed within a few months without making it contrived or using (bad) retcons. If it took several decades to developed the technology then it wouldn't be far fetched.
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Your entire argument hinges on assumptions not yet proved.
First why must the the ark project have been started during me3 why couldn't it be started just after the events of ME1? A huge "geth deadnaught" attacks the citadel and almost succeeds. What if the Geth had won? They'd have destroyed all life in citadel space. Maybe we should do something about that.
Maybe it was started and shelved during the Rachni wars and was restarted during the events of Me2?
Maybe the underlying theories of alternative FTL drives where already developed AND published by someone decades ago but with mass effect technology it was simply ignored. And don't pffft this idea either the paper that explained mad cow disease being prion was published in the 1960's. Prions were pretty much IGNORED until there was a crisis and low and behold someone already discovered them 50 years earlier but it wasn't knowledge that was needed or could be exploited so it sat doing nothing. The same COULD be true about alternative theories of FTL travel.
There is no need to cram everything into a few months just because the reaper war starts in ME3. There is reason enough to start the project right after the sovereign attack without believing that Shepard's reapers are coming. The Geth explanation is reason enough to think hey maybe we want a contingency plan in case they take the citadel. The geth have shown a willingness to let organics flee an area without pursuit so an ark has proven track record at surviving Geth expansion. This also isn't the first time citadel space face extinction and having an ark project in the works then could give a huge head start to an ark project now.
Your argument hinges on assumptions that are not only not proven but there are numerous PLAUSIBLE ways the technology and the project itself could have had a head start before the events of ME3. There is no need to assume the project and its technologies all started development the moment earth fell.