Clay definitely seems to be the surface that comes with all these answers. Carretero at Hamburg, Guga, Chang, and Wilander at RG. How about a non-clay Masters or Slam first time titlist? (Excluding AO pre-1982) I know, the question is growing more and more complicated. Becker maybe? But I think he won a title or two before Wimbledon.
Becker won Queens before Wimbledon and Sampras won his first two titles the same summer he won USO. Courier won a smaller event, then the IW/Miami double then Roland Garros. Those are the closest for non-RG that fit OP's questions that I can think of.