Just a couple of points
Is the approx DoB of Mary correct? Would she have been 16 - I note you have said in another thread that she was born c1825.
Do you have the dates of death of Thomas Cullen, Mary Nowlan/Nolan Cullen and Michael Cullen.
Are you aware of the irish naming pattern that some families used, even after leaving Ireland. it can give clues to go further back
The Irish naming pattern is as follows:
1st son is named after the father’s father.
2nd son is named after the mother’s father.
3rd son is named after the father.
4th son is named after the father’s eldest brother.
1st daughter is named after the mother’s mother.
2nd daughter is named after the father’s mother.
3rd daughter is named after the mother.
https://youririshheritage.com/lessons/irish-naming-patterns/So it may be possible that Michael is named for the father of Thomas Cullen Snr and Agnes for the mother of Thomas Snr. NB Agnes is sometimes a diminutive of Nancy, and Anne and Nancy are sometimes interchangeable.
