Hello all. There is a little bit of discrepancy here. Allow me to clear the air with the views of one who works in the biological field.
The OP mentioned that the first seven days mentioned in Genesis may have been greater than 24 hours. I believe this is perfectly reasonable. Note that the verse says "the morning and evening were the first day." Imagine you are being granted this vision or story from God. Would you not apply your own viewpoint to your transcriptions? The idea of the sun rising and setting is naturally a "day" in our view. However, our views are limited to our own opinions and experience. So the first "day" (being sun rise to sun down) could have been a thousand years. The first objection any scientist would make is that such a timeline would destroy fauna, various life forms, etc. Yet, keep in mind that death has not entered into existence, for all is still perfect in creation.
If one allows for the possibility that each "day" of creation was more than a mere 24-30 hours, then fossil records, carbon dating, etc fall into place perfectly.
Now to address the disbelief of science. Science is a study of the natural. Science cannot measure anything that it cannot collect or reproduce in a lab. Science can make educated guesses, which become theories. However, theories are not laws. Theories are just that: theories. So let us examine carbon dating closer. I use it as evidence all the time. However, as a true scientist and realist, I know that carbon dating is not perfect. For example, any sample that predates my carbon isotopes distorts an accurate reading. Carbon dating is the most accurate test we have, but even it allows for moderate error in results.
In my opinion, these items that I have listed for consideration are a component of critical thinking. One which many theists, anti-theists, Christians, scientists, pretty much any labeled group, forgoes for the sake of making their opinions and ideologies cohesive with evidence at their disposal.