Hi Lisa
Prior to 1864 and civil registration of births, deaths and Roman Catholic marriages (1845 for non-Catholic marriages) in Ireland you will have to rely on church baptism, marriage and burial registers to confirm ancestry details. Church registers are effectively the building blocks of Irish family history back beyond the mid-19th century.
In the ideal world family history databases such as Ancestry or Rootsireland.ie would record in County Antrim a baptism of John Martin born c. 1753 and the marriage of his parents, John Martin and Jane/Jenny Hutcheson c. 1752; or a ‘relative’ in the wider family history community(perhaps identified through DNA) holds information/oral traditions, documented and passed down through the generations, that sheds new light on ancestral origins.
RootsIreland.ie is the largest online source of Irish church register transcripts, but it must be emphasised that a failure to find relevant birth/marriage entries in this database (or indeed any of ‘big’ family history databases) doesn't mean that the events you are looking for didn't happen in Ireland. It simply means that they are not recorded in the database; for example, they may be recorded in a church whose registers don’t exist/survive for the time period of interest or in a source that has not been computerised. It must be said that the many church registers in Ireland don’t predate 1830. Hence the birth, marriage and death details of many of our 18th century ancestors have not survived in a written record source.
Furthermore, 'census substitutes', such as Protestant Householders Lists of 1740 or Flax Growers Lists of 1796, by naming heads of household only, provide insufficient information to confirm the nature of linkages between named Martin households in these sources. Census substitutes, however, are very useful in confirming the presence of a family name in a particular townland and/or parish, and in providing some insight into the frequency and distribution of the Martin surname in County Antrim.
In the 18th century the merchant community of Belfast, Newry and Londonderry traded extensively with the east coast ports of North America. Flaxseed was shipped to Ireland and on the return journey linen and emigrants were destined for North America.
Robert MacMaster’s book 'Scotch-Irish Merchants in Colonial America: The Flaxseed Trade and Emigration from Ireland, 1718-1775' charts in great detail the merchant community involved in this trade. It references the activities of George Galphin and his partner John Rea of Rea’s Hall, near Savannah (Georgia), who were active in the 1760s in bringing emigrants from Ulster to the Carolinas and to Georgia.