Self insurance is probably your best option here. Put a certain amount of money into a separate savings account every month and in case of a damaging earthquake, use that to recoup your losses. Yes, the "payout" won't be as high as that of a standard insurance policy, but by self insuring you're forgoing the risk pooling that comes with many policyholders paying into a fund (the insurance company) and only a subset of them receiving a payout.

As MichaelA answers, the only alternative to insurance is self-insurance.

• This is not a whacky idea. Note that it is fairly common that corporations "don't like" insurance so they self-insure certain risks: i.e., they judge financially that it's better to self-insure.

• A simple real-world example, I have never in my life bought "comprehensive" car insurance on any vehicle, anywhere in the world. {Obviously you should, and of course in most jurisdictions legally have to, buy 3rd-party insurance.†} Hence if I ever have a car stolen, burst in to flames or the like ... it's a straight loss. But on the other hand I have saved all those premiums on all those cars all those years. (If you're wondering, the outcome is I'm wildly ahead; I've never, ever had a car stolen, burst in to flames, etc - even once.)

In answer to the question at the end...

Or perhaps some sort of an insurance on the insurance that is well know to pay out quickly, ideally evidenced via their quick payouts during the COVID crisis?

Yes, in the US "Aflac" exists for exactly that purpose:

https://www.youtube.com/watch?v=Pj3B9PFNvZQ go to 0:15
https://www.youtube.com/watch?v=SaVTrV0Wsew go to 0:21

(Roll tide!)

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† Of course, if you get a car loan, you are forced to get comprehensive insurance by the loan company.