Gail,
You are looking for Thomas’s birth certificate. Going by his marriage certificate in 1881 (when he said he was 23) he was born c 1858. That’s 6 years before birth certificates were introduced in Ireland (1864) so you probably aren’t going to find a birth certificate. You might find his baptism but you would need to know which church he was baptised in. It was presumably a Presbyterian church since that’s his denomination in the censuses but there are at least a hundred Presbyterian churches in Co Derry. And few of their records are on-line. Without some idea of where he came from it’ll be difficult.
Thomas’s father is named as Thomas, a farmer. If still farming in the late 1850s, he should be in Griffiths Valuation. However there isn’t a single Thomas Telford in Co Derry. So either he had died or left that county. I searched the statutory death records for a Thomas Telford who died 1864 to 1901. There are 16 across Ireland but none in Co Derry. I also searched the statutory marriage records (which start in 1845) for a Thomas Telford who married in Co. Derry 1845 – 1865. I did not find one.
There are 2 trees on Ancestry which list Thomas & Agnes but neither has information on his place of birth.
Sorry but I can’t find any useful clues as to his origins, nor can I suggest a quick way of finding it out.