Has anyone ever won Olympic gold in both boxing and wrestling?

I don't think so. There was an American (Irish born) boxer named Joe Lydon who won bronze in the 1904 summer Olympics and silver in Soccer during that same 1904 summer Olympics. I think that was the only time a boxer has ever won multiple Olympics events ever. I don't think it has ever been done in both boxing and wrestling.

Michael Alvarado was a wrestling state champ in HS

I don't think its happened at the Olympic level. Unless it was one of those old timey mfers back in the 1930's or w/e. I'd be surprised if someone or a few cats haven't won national titles in boxing & wrestling doe. Aaron Pico has won boxing titles & wrestling titles at respectable levels (super close to making the Olympic Wrestling team & I believe he won a Golden Gloves title) & he might be the closest person to doing this in the US anytime recently. I just saw him ice another fighter with a wicked body shot a couple of weeks ago. He seems to be settling in nicely after his pro debut upset loss.

Just curious if any fighter has done this. I imagine the demands of both sports might make the feat impossible though. That's a really interesting question. I didn't Google it, trying to scratch my brain about it. I would think that probably happened in the ancient games time to time. Theogenes, maybe? But obviously that's not what you were asking. I wonder if someone did it between like 1900 and 1920? It probably would've been a heavyweight if anyone did because even then I think the weight classes were off by enough pounds to mess it up, even then.

With MMA more popular than the recent past and with both USAB and USAW based in the same building, you would think it might happen. The public schools used to have both in the early 1900s but wrestling and boxing coaches have grown apart culturally and geographically and often closed minded to each other; maybe all the fakery of pro wrestling had a lot to do with it. MMA is seeing a nice revival today and I see MMA and boxing in the same gym but never boxing and wresting, which seems silly being that it should be popular with many parents but then parents, modern schools, USAB and USAW are often just really silly.

Google that.