Specifically, James Ussher, an Archbishop in Ireland came up with the precise date of creation as 9am, October 23, 4004 BC. He lived sometime during the 1600s.

When placed into context, Bishop Ussher's arrival at this date required an immense amount of study of religious and historical texts, making his prediction, at the time, seem reasonable (remembering that he came from a far different world view and people in seventeenth century lacked most of the scientific data we have available to us today).

YEC today still use his work as a baseline for the 6000 year old Earth, although some are "flexible" enough to consider 10,000 years. Bishop Ussher was an erudite scholar (unlike creationists) and if he could come back to this century, I doubt he'd stick to his figures.

I've actually written a post where I compiled a lot of the earliest Jewish and Christian texts which comment on this. It can be found here (see the middle section, with the emboldened names).

It's a lot more useful to pinpoint when Jews/Christians started challenging the idea that the world was more than ~6,000 years old. The first challenges to this that were felt in Christendom came in the late 18th century, courtesy of the geological insights of those like Patrick Brydone and James Hutton, et al.