This is in regards to my '89 IROC (L98 engine)...

Whenever I start my car in the mornings--especially if it's cold--and try to take off, the engine will often bog down down and stumble as if it wanted to die. If I try to give it even more gas while it's doing this (yeah, not going to help, I know), I'll hear a popping through the intake. I then let off of the gas, let the engine pull back up to a normal idle, and then take off by slowly putting on the gas. Subsequent takeoffs are similar in that the engine tries to bog, but not as much. Ultimately, after the engine has run for about 10 minutes, I don't have these problems anymore.

Any ideas what the culprit might be?

 

Timing.... Once your car hits operating temp timing is advanced a bit, allowing normal operation.

Backfires through the intake are almost always timing. No other way for flame to get out short of a head leak.