Might be the VVT phasers rattling away until they get sufficient oil pressure - not a hugely common issue like on Honda K-series. I have two neighbors with Toyota 4 bangers (1 Camry with the 2AZ and 1 with a Taco with presumably the 2.7) that have the grind/rattle at start. The Taco has it really bad, the Camry it only happens every so often.
I would loosen all the mounts put a jack and block of wood underneath the engine jiggle the engine a bit then tighten them before I did anything else. Make sure you have the front and rear level either on a lift, 4 ramps or stands, you want the engine relaxed for lack of a better word in there.
Should I loosen the mounts where the connect to the frame or the bolts that go through the rubber or both? I can access the through bolts, but I'd need some help with the frame bolts.
