While scientists are extremely confident about the 13.8 billion figure...
I would dispute that.
EDIT: By which I mean, sure, 13.8 billion has got to be pretty close to being right if the Lambda-CDM model is correct, but Lambda-CDM being correct isn't something I would bet my life on. There could be some complicating wrinkles.
There is plenty of debate over the nature of the cold dark matter in the standard Lambda-CDM model. But most competing models that would result in a substantially different age of the universe (t
0) have failed to match all the known observational data, particularly data from gravitational lensing and colliding galaxies. Other extensions of Lambda-CDM typically involve parameters that leave t
0 largely untouched. So I would say that most scientists are extremely confident in the value of t
0 within a reasonable experimental and theoretical error.