The claim that the idea of long ages for the age of the Earth started with atheists trying to prove the Bible wrong has been rebutted at EvC many times.
The Geoscience research Institute was set up by the SDA church to prove creation and after more than 50 years still cannot. However in their early years they had some good articles frankly looking at difficulties.
Go to
Geoscience Research Institute | Origins and look for
vol 8 p59-71 and
vol 9 p28-51 for discussion about the early CREATIONIST geologists.
Vol 8 also has an assessment of dating techniques, vol 10 looks at the difficulties of palaeomagnetism for YEC , and vol 17 a similarly YEC difficulty of the Oklo phenomenon.
And these articles are from an organisation looking for YEC evidence.
Edited by Adminnemooseus, : Add the more specific links.