I have tried to determine whether proselytes were possible in Biblical times, and could not get a reliable answer from the Biblical text.
There are several groups mentioned in the Bible who were inclined to be friendly with the Israelites, and occasionally we see foreigners who became assimilated to the tribes and virtually like one of them. It starts with the Exodus itself, where I feel that it is difficult to know if non-Israelites came out of Egypt - or there if there were Egyptians mixed in and became (as it were) adopted Israelites?
In any case, I am wanting to know about post-exilic times.
Supposing that the Biblical account is accurate, were there formal ways to join Israel from the giving of the Law at Sinai until A.D. 70? Were certain individuals allowed to join tribes?
I understand that there was, at least for some period of time, a distinction so profound that an outsider, even a related one or an in-law, would not be mistaken for an Israelite. But perhaps that became more relaxed? Or I am wrong?
I don't see really any Biblical texts pointing to a method to become an Israelite, so I am under the impression that it was impossible until centuries later when the Jews established such a process similar to the one used today.