Is it possible to get stuck with a block that nobody can mine?

Is it possible to get stuck with a block that nobody can mine?

The hash of a bitcoin block is generated from:

  1. Block version number (partially fixed*, 4 bits)
  2. Previous block hash (fixed, 256 bits)
  3. Merkle root (not fixed, 256 bits),
  4. Time (not fixed, 4 bits),
  5. Bits (partially fixed*, 4 bits),
  6. Nonce (not fixed, 4 bits).

So, the block hash is generated from 528 bits. You can change 264 bits freely to try to have a hash that matches the current diff, and 264 bits are immutable.

Is there a property on the SHA-256 function that asserts that on these 264 bits of freedom, one combination will give us a hash that is matches the diff requirements?

If not, does that mean that the blockchain could get stuck on a block because nobody can mine on it?

* "Partially fixed" values could be overriden by software updates for example. I assume that partially fixed values are fixed to simplify.

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