The APU or external pnuematic cart supply the PACKS on ground. The PACKS have nothing to do with engine start but rather are only used for air conditioning on ground/air, and cabin pressurisation (controlled ofcourse by the CPC's). During engine start, as correctly pointed out in previous posts, PACKS automatically close once ENG MODE selector is at IGN/START, and open automatically 30 seconds after the second engine's N2 reaches 50% (on V2527 IAE engines).
The fuel pumps however need to be on for engine start as you would get the associated FUEL PUMP 1+2 LO PRESS ECAM.
Cheers