I believe it came from American revival preachers in the mid 19th century.

Those tent-show snake-jugglers have a lot to answer for.

No one believed the Earth was 7,000 years old in the day.

Before the Victorians like Lyell started doing paleontology in a disciplined way, even many educated Christians believed the age of the earth was a few thousand years. They explained geology in terms of cataclysms-- floods, voclanism, earthquakes, etc; Lyell changed the timelines by reasoning that those cataclysms were no more frequent in ancient times than they were now, and that much of geology was instead driven by very slow natural processes.

Among non-Christians, some ancient Hindu and Buddhist writers speculated on the age of the earth and the universe and came up with enormous numbers, but without evidence. The Buddhists' point wasn't to come up with an accurate number, it was more that, even if the universe was really old, it wouldn't last forever because nothing does. Impermanence is a feature of being.

And as I recall, the pre-Socratic Greek philosophers were all over the map on the age of the earth, as they were on many fundamental questions. They were highly entertaining, but also highly speculative.