Some related questions: did people latch onto the 6,000 year value like many Christians do today, and if so was it considered heresy to believe it was older than 6000 years old? Did scientists and laypeople have different ideas?
It was widely believed, even among academic circles to be roughly ~6,000 years old. A "scientist" even stated, to the day, the age of the Earth (can't remember the name, but it is state in the first link below). It wasn't until the fields of physics and geology started to emerge did we start to get estimates of the age of the Earth that conflicted with theological teachings. One of the first was when a physicist (again a name I can't remember, but I believe is stated in the second link) estimated the Earth to be roughly 30 million years old. He arrived at this estimate based on how long it would take the planet to cool from a molten state resultant of its creation. His estimate was (wildly) off because at that time science did not yet know of radiation (which is the cause of much of Earth's internal heating).