Sloan is a very common surname in Co. Antrim. Looking at the 1901 census of the county there were 733.
Birth registration didn’t start in Ireland till 1864. Your ancestor was evidently born in the late 1700s. For that period you need to rely on church baptism records, where they exist. You haven’t said what denomination your ancestor was but the majority around Ballymena in the 1901 census were Presbyterian (as was most of the population of that town). Unfortunately none of the Presbyterian churches in that are has any records for the 1700s. The oldest are Ballymena 1sts and they start in 1812. The Church of Ireland has records from 1789. It might be worth checking them on the off-chance. There’s a copy in PRONI (the public record office) in Belfast.
That apart I’d say your chances of finding any trace of your ancestor are slim, due to the lack of records for the era you need.