You can initiate a probate proceeding yourself, but it might be a waste of your money ... the court filing fee is approximately $375 and you will need to file a "Notice of Probate" (using the court-mandated format) in a local newspaper that has been designated by the Court as a "newspaper of general circulation". You will also need to notify all of his nearest living relatives (sisters, brothers, children of deceased sisters & brothers).
You can do this yourself - I doubt that a lawyer would be interested in assisting you unless you are able to show to a 99.99% certainty that you are entitled to a share of the estate (since the law prohibits a lawyer from collecting a fee in a probate matter unless the Judge okays it).
You can find out how to probate an estate by consulting Nolo Press's book on California probates, which is probably available at your local library. Be aware that the court-mandated forms change every January 1st, so you'll need to get up-to-date forms or your petition will be rejected.
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.