Amplifier gain too HIGH?
It's not amplifying, it's oscillating-  that's why you get the slow build-up in the envelope.

It is possible to get higher than expected gains from an amplifier by the use of regenerative circuits-- in vacuum tube circuits a 'tickler coil' was used (cp. tickling the dragon's tail). The idea was to have the circuit close to oscillation, but not quite, so the signal was effectively amplified multiple times. 

As in your oscillating circuit, the high steady-state gain would take many cycles to build up and approach the final value.