Can I shop for title insurance? Do I need lender's title insurance with cash purchase

[Lilly Fang]

I am in Nor Cal. Usually, it costs me $3000-4500 for title and escrow. However, I am buying a Nor Cal house from PinPoint Offers right now and just found out the title and escrow cost $8100! They selected a So Cal title company and a escrow company and said it's too late to change now since we are going to close on Monday.

I am purchasing this house by cash, and I see they listed the lender's title insurance for $1650. My plan was BRRRR. Do I need the lender's title insurance for now? I think I probably need the lender's title insurance later when I refinance. Fidelity National Title charged me $1100 for the lender's title insurance for my last property. Can I shop for title insurance later when I refinance? Or do I have to use the title company and their insurance quote now, even if I pay cash?