The insurmountable problem ?

I am almost certain we are connected to a brother of the 1704 female Gatty ancestor my father's dna match is related to. By process of elimination that leaves 2 brothers born 1683 and 1690. The problem ,which seems insurmountable , is linking back that far to verify that. I am stuck at my 4th great who was married at Liverpool in 1810. Neither Ancestry or Family search offers up a likely baptism/birth . Thus there is at least a 120 year plus (roughly 4 generation) gap to be filled.