I can't speak to opening an account before you get here - my fiance and I are waiting until he's here to get him added to accounts and getting new accounts open. He's planning to use Wise (sp?) to transfer funds. I know some banks are pickier about proof of identification - and this is made easier by having a social security number.
In terms of buying a home I can offer a few tips, though.
Start building credit as soon as you have your SSN. Easiest way to start is to be added as an authorized user on your spouse's credit card (IF they are a responsible credit user). That will help you get a credit file started - which will help you get your own credit card and other LOCs down the road. This is important because when buying a home mortgage lenders will take the lowest credit score of both of your scores - this is used to price your loan and will determine how much you can borrow from the bank and with what downpayment.
Ensure you engage in traceable transactions and money moves. Yes - some lenders want to see a banking history, however this is most impactful when it comes to the funds being used for your downpayment. Bascially - if you have funds you are bringing over that you want used for a portion of the downpayment, ensure that you have a paper trail for the funds. Cash transactions do not create a paper trail.
I hope this is helpful.