No don't think it was a secret. Not when it was an open recruitment with hundreds if not thousands of personnel involved. Plus construction of the Nexus and Arks cannot be kept secret for so long.
And I think the Andromeda Initiative started as far back as after ME1 and through MEs but launched post ME2. Timeline wise: between ME1 and ME2 is 2 years. And between ME2 and ME3 is 6 months. Probably all pushed by Shepard since he is in this trailer:
https://www.youtube.com/watch?v=vZ7tGg_JIZg
Edit: the Andromeda Initiative launches just after the ME2 Arrival DLC conclusion - which is basically about the prelude to the Reaper Invasion in ME3.