My Great Grandfather, John Woods, was born in Clark County in 1878. They didn't issue birth certificates back then, but he likely needed one for Social Security. The State of Missouri issued him a delayed Birth Certificate. It has his parents and references his marriage date and place.
My point is that if you are looking for information on a relative born before birth certificates were formerly issued, you might still apply for one and see what turns up. You have to apply the old fashioned way. Nothing on-line.