The priests originally filled out a book for births and baptisms and that has more information.
Every year at the end of the year (or more likely, at the start of the next year), the priests had to extract the birth date from the birth/baptism book. It didn't include the baptism date or the baptism witnesses. That is the one you saw on Genline.
Arkiv Digital has the original book, which includes both the birth and the baptism.
I suppose the priest kept after the girl and finally she gave up the information about the father. You are lucky.
The name is absolutely not Sundgvist. That is not a Swedish name. It has to be Sundqvist.