Sure, to add to what Shirley T. and Ted Pack have said, it's entirely possible for someone born in 1888/1889 to go through life without a birth certificate. My parents were both born at home in Texas in the small towns of Frost, Navarro County, and Grapevine, Tarrant County, in the years of 1920 and 1925 respectively. A physician attended each birth, and both sets of grandparents would have been considered middle to upper-middle class. My dad's birth is particularly memorable because the doctor wouldn't let my grandfather come downstairs to see the new baby because he had the flu (as part of the worldwide pan-epidemic of influenza). The general practictioner who diagnosed my red measles at age seven (when we were visiting my maternal grandmother during the Christmas holidays) attended my mother's birth.
My dad had finished college and law school, was drafted and shipped to Europe, and had worked as an attorney for 40 years before he obtained a birth certificate. My mother also had graduated from college, had taught in the Texas public schools, and had given birth to two children before she obtained hers.
To make a long story short, my mother talked my dad into taking her to Europe in 1981 (he didn't want to go, having seen it all before in World War II). To obtain a passport, each had to have a birth certificate. In both cases, older brothers (either age 5 or age 10 at the time of each parent's birth) swore that they remembered it. Both births were also recorded in family bibles. It was a different age--my oldest maternal uncle, then age 10 now age 93, claims he didn't know my grandmother was expecting until the children (aged 10, 8, 5, and 3) were shown their new baby sister.