Legal Question in Civil Litigation in California

You can certainly make the request, but it will almost certainly be denied. The court likely will take the position that everyone is present to go to trial, and that you should have made the request weeks or months ago. It may also state that it has no one available to perform the mediation or evaluation.

Mr. Perry is entirely correct. If you have a trial date then you had months of time and at least one case management conference to request the mediation or other ADR procedure. This has less chance of success than your last idea of asking for time to retain counsel when you've done nothing until now.