Year of car? How many miles?
After first start I put it in gear about 2-3 seconds later to back it out of the garage, push garage door button and verify door closure, back out the rest of the way to street. Then off we go. 10-15 seconds elapsed time approximately.
A variety of possibilities and we'll need more basic info on your car. Tranny fluid maintenance done recently? Engine or tranny mounts replaced? Any other odd running issues occurring?