If P = NP, how do I prove I can find the maximum clique in polynomial time?
Assuming $P=NP$, then $CLIQUE \in P$, so you can test for a clique of size $k$ in polynomial time for all $k$. So you can just test for a clique of each size between $1$ and $n$ where $n$ is the number of nodes.

Now that you have the max clique size, you just need to find it. You can do that by removing an abitrary node, then re-running then seeing if there still exists a clique of max size. You will be left with the max size clique.