All of the below is just my own personal opinion and not to be taken as legal or financial advice.
When you win, there are two concerns for the casino to release your money. First is taxes and the second is getting the money to you. The money part is easy, they will basically give it to you however you want. You can take a check, chips, cash, a wire transfer, a combination of all of those, etc. But before any of that happens, they want to work out the taxes.
Basically, they want to make sure that there is a federal number assigned to you so that they can tell the IRS (the US tax agency) that they paid X money to you and that they either collected the tax or they need to go to you to collect the tax. In the case of US residents, we have a Social Security Number (SSN) and once you give that to the casino they release your money.
As for people who do not have a SSN, you can get what is known as an ITIN and that will serve as a valid number that you can give to the casino. An ITIN is also issued by the IRS and you can get one online in just a few minutes.
Of course, all of the above is just my own personal opinion and not to be taken as legal or financial advice.