In Bitcoin, what happens if there is no viable nonce?
It's important to note that the block hash is over the entire block header, which contains:

Block Version
Nonce
Previous block hash
Timestamp
Merkle Root
nBits

Of these, only the nBits and previous block hash are fixed - all of the others can be manipulated to alter the hashed data at will.
Once all 32 bits of the nonce value have been exhausted (which happens extremely fast on ASICs), miners will simply alter the timestamp, block version, or merkle root (by altering the coinbase transaction or changing their list of selected transactions/their ordering), allowing them to try a new block header with the entire nonce space again.
These alterations are repeated until some combination of the above produces a valid block hash.