My perspective may be different than most because I was a young-earth creationist for a good part of my adult life. Sadly, I wasn't much for hunting the truth, I was happy to accept my faith and trust in God.
To be honest, I didn't really think about it much until later but was a fairly fundamentalist Christian, accepting the Bible as inerrant, special creation, and even "speaking in tongues" which is also part of scripture. So when presented with the argument that we must believe Genesis literally, including that the Earth is young, that seemed like a natural. I had nothing vested in evolution or the age of stuff so it wasn't a big deal. In fact, it was fairly easy to accept the arguments presented by religious sources and look no farther.
That changed when a series of events led me to first doubt my beliefs about creationism then discover that they were pure and utter fantasy. Through the help of an Australian friend who answered some of my questions with specific examples, and the "Evolution 101" podcast of Zachary Moore, I realized that I'd been hoodwinked.
I was pissed.
It turns out that the scientific evidence for an old earth, for an evolutionary progression of life, and the validity of dating methods, is extremely well understood and well accepted by essentially everyone outside of religion. It says a lot that 95% of all working biologists accept evolution and an old earth, but it says even more that the remaining 5% are almost exclusively defending their religion. That's not science.
Geologists are another group that overwhelmingly accepts a billion+ year old earth. It's telling that even most Christian Geologists accept this as apparent by looking at the Affiliation of Christian Geologists website. Here's their statement about an old earth.
Since tossing the "god glasses" I've been thrilled to discover an incredible world of science that, as a method, has advanced our capability in everything from feeding a growing population to making really cool stuff like cars and powered paragliders. I've also learned that there's quite a science behind belief.
When someone has lots of social connections they are looking for ways to reinforce their core beliefs. That makes sense, of course, nobody wants to think of themselves as "close minded"; we want to think that we have good reason for those beliefs. So we seek out "supporting" evidence which is exactly what I did.
Answers in Genesis was where I turned for those questions that seemed intractable. And frequently their non-answer was disappointing but I always chalked it up simply not knowing the mind of god. "We'll find out in heaven" was a common refrain. It wasn't until my social circle changed that I was able to finally start looking elsewhere. When my Australian friend questioned my blind belief in a friendly but direct way, and I had no good answers, I started looking at other evidence.
Wow. That evidence is truly overwhelming for those who are interested in knowing, not just believing. It takes a lot but the trappings of reality are worth the journey.