Found it now.Baptism 18th December 1873https://registers.nli.ie/registers/vtls000632945#page/62/mode/1upBirthhttps://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1874/03157/2158053.pdf
Looking for information on Andrew Briggs who would have been in the Portumna, Galway area in the 1870's. He is listed as the father of Andrew Nolan (born 1873) along with the mother Mary Nolan at the baptism but not on the birth register.
You seem to be assuming that a baby was conceived in the same place as it was born. Mary Nolan may have gone away to work, become pregnant and returned (or gone to Portumna) to have her baby. Or she may have met her swain at a fair or on a trip to the seaside or while visiting relatives.