I am a NON US resident but I have a SSN and I formed an LLC in Wyoming. Do I need an EIN or I can use my SSN?

You need to register for an EIN from the IRS before you start cutting paychecks and withholding taxes for your employees. In the US there is a layer of Federal requirements on top of the state-level requirements, and this is one of those cases: there’s not going to be a Wyoming-specific EIN but instead an EIN from the IRS. See irs.gov for the online form.