You can fly to the US (after corona limitations are over) and open a bank account in a retail branch.
Why did they reject it?
Maybe you just need to make the effort and create a nice home page, create an email account with the page address, so no protonmail etc., get a US phone number and then you should be good to go.
Also think about registering in a different jurisdiction, because I guess you have chosen the anonymous New Mexico LLC which banks don't like. You will have a higher chance for a Mercury account with a Delaware, Florida, Wyoming etc. company. New︀ Mexico and Nevada are frequently declined.