Storm in a teacup. OP has a baptismal record, so what is the problem? A real problem only occurs when no record at all can be found. Which is all too often.
People don't seem to realize just how many births and deaths were not registered! (Or registered many years late).
That said, a marriage I know was registered, because it is in the index, but does not appear - for some unknown reason - on the Irish Genealogy site. So, the index should be checked as well as looking for the actual registration.
As for not finding any record of adoption, well of course not, there are no such records.
Apart from that, the birth was not in "Northern Ireland". There was no such place at the time.