You make a fool of yourself in Los Angeles.Then can you ever start a career in Hollywood?
On the contrary. It's a prerequisite.
Your question is a paradox. You make a fool out of yourself in acting classes. That's where you learn to uplift all the barriers and just let go. That's also where you "start" an acting career - acting school. Quality training. As well as low-level experience which may or may not have you make a fool out of yourself. For those two reasons, if you can't even do it in acting classes, if you can't let go and you get embarrassed, you can't be an actor to begin with. That's part of the craft and the job.
Being willing to take risks and make a fool of yourself is one of the very first things that any actor learns at drama/acting school. As long as whatever you did wasn't dishonest, racist, homophobic or otherwise nasty, and you haven't proved yourself to be a bad actor or unreliable, having once looked foolish wouldn't make any difference.
How many actors/actresses have not publicly made themselves look foolish?
Depends on how big.