He is not eligile for federal mean-tested benefits, however, you are eligible. Signing of an Affidavit of Support only covers initial 5 years of LPR. One of the conditions of SNAP is that applicant must have been an LPR for five years. Exceptions apply in case an applicant falls within a federally protected class.
Read Section 403, subsention b and c.
https://www.ssa.gov/OP_Home/comp2/F104-193.html
What do you means by EBT? EBT is just a card, it is like a debit card, what mean-tested benefit are you seeking?