Can a PF cake become contaminated after birthing?

Yes, it can. The most frequent contaminant to encounter at this stage is green mold and it seems to happen more often if the cake wasn't colonized throughout, the cake was already contaminated during the incubation phase or if the cakes are handled at birthing with dirty hands or tools.

Usually though the cakes only contaminate after a few flushes when they are exhausted.

Make sure to separate a contaminated cake from the others as soon as possible and to discard it outside of the room you use for growing to prevent the mold spores from spreading.