@Amy Wei Ru Chang, LA investor and Realtor here...
I think you should use $300K as a down payment and borrowing the rent of the purchase price. If you have income to support the loan, your purchase price is now $1.2M.
Then, use the other $300K to build an ADU or two on the property you buy. Adding ADUs to existing structures is the best investment you can make in LA right now -- especially if you have the cash for it. The additional income from the ADUs will easily cover the cost of the loan and produce really solid cashflow. Plus, buy in a rapidly appreciating part of town, and you'll really reap your gains when you sell or refinance down the road.
Here's an active property that I love right now:
https://www.redfin.com/CA/Los-Angeles/1167-Geraghty-Ave-9006...
Very affordable (for LA standards) and in the improving neighborhood of City Terrace. What's more, there's a garage with a basement underneath it. The garage and the basement can each be converted into studio ADUs, and I think the price tag would be around $300K. Converting the garage and its basement into two studios would generate about $3500/month in additional cashflow.
Happy to discuss more if this kind of a strategy piques your interest. It's the kinda of thing you can only do in LA (because of CA's ADU-friendly laws and LA's HCOL), and it's a real game changer here.
Good luck!
Best,
Jon