Can some of the cake elements be prepared ahead of time?

Yes, you can prepare the buttercream and sponge cake ahead of time.

Buttercream: Make the buttercream in advance and freeze it in an airtight container. To use it again, thaw it completely to room temperature and whip it in the mixer until it reaches a usable texture. If you try to mix it before it is fully thawed, it may split.
Sponge cake: Freeze the sponge cakes and defrost them overnight before decorating.