This is an old suggestion of Joel David Hamkins at the end of his answer to this question: http://mathoverflow.net/questions/29945/forcing-as-a-tool-to-prove-theorems I just noticed it while trying to understand his answer. But indeed it would be nice to have a big list of $ZFC$ theorems that were proven first by forcing.
A very well known example is Silver's Theorem about the fact that the $GCH$ can't fail first at a singular cardinal of uncountable cofinality (say for instance $\aleph_{\omega_1}$), I had read somewhere (Jech, maybe) that Silver proved it first using forcing.