This is Lana from Shopify.
I understand this is a frustrating situation. When it comes to third party gateways, while we are not able to influence their decision in any way, I can make some suggestions and try help you find a different gateway!
There are a number of reasons as to why you might not be eligible for a payment gateway, and one of the main ones is the country in which you are based. You will find that not every gateway is supported in every country, - in which case we have an information page with all supported payment gateways on Shopify which can be sorted by country. There, you will be able to select your country from the list when you scroll down, and you will be presented with all available options to you.
Once you have found something from the list that you think will suit you, the first step is to go to their website when you get set up. If you run into trouble or if it gets rejected again, I would recommend you contact the support of whichever gateway you have chosen to see if they can provide some clarity on that.
If you're able to set up an account with a gateway successfully, the next step for you is to integrate it with Shopify. This can be done by following these steps here.
Once you're all set up with the gateway, have you already looked at other aspects of your store to get ready for launch? If you're not sure where to start, you can check out our Shopify Blog article on The Store Launch Checklist which can take you step by step through everything you need to do before you're ready.
If you have any other questions on that or anything else, please do let me know.