Obtain Letter of Testamentary without Probate

What is the name of your state (only U.S. law)? California
My husband passed away leaving only a handwritten will (not notarized). I now have all of our assets (including my home) in my name except for one investment portfolio worth $30K.
The investment company needs a Letter of Testamentary in order to transfer that portfolio to me.
How can I get this letter without going through probate?
Is it enough to submit

Why would you not want to go through probate? That is the only way that it can be distributed to the legal heirs, whoever they may be. That is your only option here. Most counties have inexpensive, simplified procedures for smaller estates. As soon as you or your attorney files to get probate open, the court will issue the letters testamentary.

The investment company is very, very wrong.

There is no probate (administration) in California for assets passing from one spouse to the other. Asking for a court order saying you own the account is an optional procedure, and in this situation, IMHO a waste of time and effort. But some "holders" are obstinate.

Look at Probate Code Section 13500 for the rules, and 13650 for the optional procedure.

If citing these statutes gets you nowhere, you might consider hiring an attorney to send a stern letter before you seek the court order.