Libby, the discoverer of the C14 dating method, was very disappointed with this problem.
He understood that archaeological artifacts were readily available.
After all, this what the archeologist guessed in their published books.
Some believe trees are known to be as old as 9,000 years. A lot of people doubt this claim for various good reasons I wont go into here.
The ratio of radiocarbon to stable carbon atoms in the atmosphere has varied in the past.