It depends upon the "smoke." If the smoke lingers, it could be oil smoke, usually bluish in color and an oily smell. If the smoke is white, and has no odor, could be just the condensation burn-off from the exhaust system.
When convertor, pipes, and muffler cool down from being hot, condensation is formed. As the engine heats up the exhaust system, it burns off this condensation and becomes a vapor, hence, "smoke"
It also may be sucking the oil from the intake runners. This oil seeps down the valve stem and lays on the floor. Engine cranks up, creates a vacuum, sucks up the oil, then as the engine warms up, seals get lubed, oil supply stops. Maybe.
I would suggest a can of GM Engine Oil Supplement, made for your situation as well as others if you think it is oil smoke.
Everett "OBJECTS IN THE MIRROR APPEAR QUICKLY UPON RAPID DECELERATION"