We at Advanced Targeting Agency are finishing up our first EBT/SNAP integration. As N_Abey has mentioned you need a gateway payment processor. It took a while, but we teamed up with a world-class gateway payment processor, published the API, and are rolling it out on Word Press and Shopify. With the API you can integrate it yourself or hire N_Abey. I recommend you hire a third party like N_Abey because it requires a little extra programming. We get a referral credit, so, email mail me at email@example.com and I will introduce you to the payment processor.
Can you drop me an DM or share your contact details. we will send you next few steps.