Mining is pseudo-random - not fully considered random.

It's a mathematical function that 'could' be solved to pre-determine the results - but alas it's beyond anyone (so far) to actually do that, so for all intents and purposes, the sha256 hash value result of the 80 byte block header is random.

In truth, nothing is random, but the universe is way too big to be able to monitor every particle to pre-determine the outcome of events even as simple as rolling an unbiased dice.