Sounds like a catastrophic vacuum leak to me, or it's not sensing intake
air volume correctly, as you said...Make sure the PCV or other large
vacuum lines aren't unplugged, depending what motor you have it could
have a massive intake gasket leak...

But you're on the right track, they throttle way up like that when
there's too much air in the cold start mixture. Could be the IAC also,
not being able to get it into a rich cold engine start idle...can you
keep it running by giving it throttle or no?

EGR stuck open would also do this...

Well you can rule out the O2, because it ignores that signal until the
engine warms up.

What you need to find out here is if it's too lean or too rich that's
causing the condition. When you say it runs up to 3000 then dies, is it
smooth and strong sounding until it checks out?

And does it woof and backfire through the intake when you try to keep
it running with the throttle? Or just chug like it's flooding? Any
sooty exhaust as it dies out?

A defective Coolant Temp Switch will sometimes make something like this
happen on cold starts, but usually causes overfueling and sooty exhaust
and strong fuel odor, along with fuel fouled plugs.

The MAF could concievably cause this, you can have someone thump on it
while you attempt to start it, if it reacts to being bumped, it's
bad...

The 3.4's did have lower intake gasket design problems, sometimes the
gasket would disintegrate and cause leakages. Usually there was coolant
loss involved too when this happens.

This is the SFI SOHC 3.4, right? Not the DOHC? I don't even know if
they put those in Grand Prix, but they were a headache.