Well, he could probably take a DNA test on a commercial ethnicity website, (you can also usually transfer the raw data onto Gedmatch, and check to see if any matches with even more people, who might have taken a test on another website) and if he has any matches with people who have Native American that are super closely related, can reach out to them and ask them who they are and if they might know of any family members that had a child given up for adoption. If you can figure that out, can maybe see if they are part of a tribe, and which one. Other than that, only probably could find this out from the adoption paperwork, but some adoptions are closed, and so they have some contract with the birth parent(s) to not disclose their identity, even if requested.
That said, I find this highly unusual. Most tribes do not allow out of tribe adoptions. It's considered a "last resort" if they absolutely cannot place the child in a Native-family home, either as adopted or foster home. This is actually even codified by law. In 1978, Congress passed the Indian Child Welfare Act, or ICWA. The ICWA mandates that when a Native American child is put up for adoption, or in the case, if a parent dies, exhaustive efforts must be made to reunite the child with the surviving parent or other relatives. Children are placed with non-Native families only when an Indigenous foster home, preferably one within the child’s tribe, cannot be found. Here's the law, verbatim:
"25 U.S.C. § 1915. Placement of Indian children
(a) Adoptive placements; preferences
In any adoptive placement of an Indian child under State law, a preference shall be given, in the absence of good cause to the contrary, to a placement with (1) a member of the child’s extended family; (2) other members of the Indian child’s tribe; or (3) other Indian families."
So I presume your father was born after 1978, or was in a small tribe, and didn't have anybody who was able to adopt him, and/or just too small for it to allow enough distance between the natural and adoption parents or without the tribe's permission or something.
You could probably contact a lawyer who has knowledge of Tribal law, as they may be able to provide you more information about this. I mean, there is technically "rights of benefits" that your father could be entitled to if he would have otherwise been a fully-fledged member of a recognized tribe, and was removed improperly without their permission, and perhaps if that happened, they would allow him back in, and could have a legal claim to any such benefits he would have a right to receive, had he not been taken from his tribe. Just a thought, if something happened under less than legally prudent circumstances...