Olivia here from the Shopify Team.
Thanks for sharing your question with our network. To dive right in, you are correct that it's not possible to integrate with any third-party payment providers that are not available in your region. For example, you can find the list of available payment gateways in the United States at this link:
If there is a gateway you'd like to see on the list, please share it with me and I'd be happy to send the feedback to our product team. Furthermore, it is certainly possible to set up manual or alternative payment methods as a potential solution.
You can set up an alternative payment method to allow your customers to pay for their orders online using something other than a credit card. For example, cryptocurrency is a popular option that allows your customers to pay without going through a bank or another institution.
When your customers use a manual payment method, you can arrange to receive their payment in a way that works best for them. You can email an invoice to your customer. After you receive the payment, you can then manually approve the order.
Common types of manual payments include:
It sounds like your client has gift codes created outside of Shopify that they would like to use? Let me know and I might be able to help brainstorm further.