Incorporating in Wyoming creates your company. The licensing analysis comes separately. Choosing Wyoming as your corporate home does not settle where you may offer regulated payment services.
If your activity requires a money transmitter license, you need to examine the states involved in that activity. A Wyoming license does not automatically cover transactions involving customers elsewhere. For example, Texas regulates relevant money-services activity offered to Texas residents even when the business has no physical presence in Texas, subject to its exemptions and other permitted structures. Texas licensing guidance
The first thing I would ask you for is a detailed flow of funds. “We are a payment gateway” is too broad. Does your company only supply software? Does it receive money? Who controls the account? Who owes the customer the payment, and who settles with the merchant or beneficiary?
Map every transaction scenario, including refunds, intermediaries, and settlement. Then identify where the relevant parties are located and which entity performs each function.
That gives us a basis for deciding whether you need your own state licenses, can operate under a properly appointed authorized-delegate arrangement, or may qualify for an applicable exemption. It also helps determine whether Wyoming is a sensible corporate location for the business.
I would make the operating model clear before selecting a jurisdiction because someone described it as easy or inexpensive. The company formation is only one part of the work.