For AM's Gen3 tape-out happened around mid to late January 2014. Testing was done on March 28th/29th. So that was approx. 8-9 weeks from tape-out (which is very quick). I am not an expert in this field but others stated that this normally takes a minimum of 3 months.
EDIT: To avoid any misunderstandings:
http://en.wikipedia.org/wiki/Tape-outI think you should also mention when was the first miner running and when sales started (which was ~2 months after the first chip demo)