Can I find a number, such that the its SHA-256 hash is all-0 I want to find a number, such that the result of its SHA-256 hash is all 0.
I don't know if this number exists.
For any output $z\in \{0,1\}^{256}$ it is very unlikely that there is no input mapping to it, since the input space is astronomically larger than the output space, and SHA256 has been carefully designed as a pseudorandom function. So, most likely yes such an input exists.
The number of trials you need to find such an input (no shortcut better than trying random inputs is known) is approximately $2^{256},$ this is the first preimage problem in hash function theory.