Local cache of events (really a projection) after archiving events

This is a hypothetical scenario at the moment (at least for me)…

I have a few events that I listen to build up a local working cache of data that I use to issue further commands within the system.

I also take snapshots of streams at certain points and archive events that take place before that snapshot.

If I want to rebuild that local cache, how would it deal with snapshots on those particular streams when it’s only catching up on events within the system?