I'm here to help you get pointed to the right direction to get assistance with processing payments in QuickBooks Online.
Processing payments in QuickBooks Online without having/entering an SSS of ITIN is possible. In doing this, you'll need to reach out to our Merchant Services Department. This way, they can conduct an account verification and provide you the best option of handling payments.
To give you more insights with QuickBooks Payments you may check on this link.
You can always reach back out to me if you have any other concerns with QuickBooks. I'll be around to lend a helping hand. Have a lovely day!