We might want to distinguish between "can" and "should" at this point. As far as I know, the A/P allows engagement immediately after liftoff. The mode will be track hold (laterally) and a combination of V/S and speed (vertically) until LNAV and VNAV kick in at 50' and 400' respectively.
Some don't have much faith in the A/P at low altitudes and leave engagement until later.
I assume we are talking about the 747-400 and not earlier series 747's or the 747-800?