How do genes evolve a new function by point mutations

I am trying to understand how new genes arise. As I understand, new genetic material can be created through duplication, gene transfer or similar, which can then freely mutate.
What I can't wrap my head around though, is how it then gets to a gene that has a new specific function.
Here lies my Problem: the function is determined by the structure of the corresponding protein, which is highly specific and it must evolve by point mutations.
How are point mutations selected for, if a big structural change requires many mutations at once?
Take for instance a neurotoxin. If there insn't already a gene with a similar function, how do we get to its highly specific structure by only minor structural changes, which have no immidiate advantage?
I might have a completly false line of thinking, but i couldn't find anything on the topic. Thank you for reading, I would welcome a detailed answer.