Split the down payment and make two smaller down payments on two separate houses, a year apart (I think that's the limitation on FHA loans).

I recently purchased a home in a small town within it's city limits.

That in turn limits me to about 1-3 deals a year while I wait for equity to build.

This limits my options significantly.

Problem is that starting out you don’t really know or have access to these deals due to your limited network.

It's easiest for me but there are plenty of other competitors with similar products, for what its worth.I used a commercial loan and an LLC to limit liability. 

Essentially legging into a property for limited down payment?

Also, don't limit yourself to just Cali's inventory.

@Eric TanJust based on the limited info, I would structure a Lease with an Option.

Some HOAs put restrictions on the number of rentals in a given community (such as 30% of the community can be rentals while the other 70% must be owner occupied), and once that limit is reached, the HOA won’t allow another rental.