How soon can an executor distribute funds from a trust in California?

What is the name of your state (only U.S. law)? California

My grandmother died less than a week ago and the executor is already disbursing checks. I heard at least a month has to pass before any disbursements checks can be made to beneficiaries. Is this true for California? What is the necessary amount of time that needs to pass before disbursement checks can be issued?

A trustee administers a trust - not an executor.

I am not aware of any "waiting time" mandated by California law. Unless the trustee is intimately familiar with all the financial details and any liabilities, it may be unwise to make distributions so quickly. But, that is the trustee's decision... and the trustee's problem if something unexpected comes up.