At the first school I went to (about 60 years ago) :o I remember watching a mound grow in the playground in the tarmac worn smooth over years of tiny feet. Eventually this mound cracked and out of the top grew mushrooms!
If flippy floppy mushrooms can push through tarmac, your spuds will have no trouble pushing up through a bit of 'firm soil'. :D
Cheers, Tony.