There are no easy solutions. Only a tiny handful of churches in Co Antrim have records for the early 1700s and late 1600s (Probably fewer than 20). Most churches early records have been lost over the years for one reason or another. There are a few estate papers for wealthy landowners, and a few legal papers for people who were otherwise notorious, and there’s the 1669 Hearth Money Rolls for part of the county (which contain no Roberts). That’s about it. The advice you have been given about the more or less complete absence of records, certainly for the average man or woman, is correct. There’s nothing to look up and no real way round the problem.
Roberts is not a common name in Co Antrim. Griffiths Valuation (1847 – 1864) lists just 17. Most were in Belfast. Though they could have been living there in the late 1600s and early 1700s, the population wasn’t very big then and really only increased during the industrial expansion of the late 1700s and 1800s. So it would be dangerous to draw any conclusion from that source alone about Nancy’s origins in Ireland.
With Roberts being essentially a Welsh name, it’s likely that her ancestors probably came to Ireland in the Plantation period of the 1600s. So they probably hadn’t lived in Ireland all that long when they left again for America.