That's where trusting something (or Someone) more than human intelligence comes in. Natural phenomena can be verified through visual observation and study...but since God is invisible to the naked eye, His existence must be approached first through the spirit, not just the mind. After that, we can see His handiwork in nature, but we will always be limited when compared to Him.
On certain levels, humans can only understand and comprehend so much about God, because we are mortal. We are bound by time and space; He is not. God is higher, more powerful, and vastly more intelligent than any of us...so on that basis, how could we hope to understand Him in total, with just our mortal mind? We can't; He gives us the knowledge and information we need to trust and have faith in Him, but not necessarily to finish the "great puzzle" on our own. After all, if we were capable of doing everything by ourselves, we wouldn't need God. As a responsible and just Father and Creator, God has made sure we'd have to come to Him for various things.
Now, let me explain this: God is not stupid, and as a race, neither are we. He was brilliant enough to make us in His own image, but sin corrupted our nature, in more ways than one. It's very likely that humans were much more skilled (and had greater insight) thousands of years ago, than we are today. The pyramids of Egypt are just one possible example of how advanced "pre-modern" humans really were.
If you're referring to the rock layers and such, then answer this: how can upright trees be found, passing through multiple layers, and they're intact? If each rock layer were truly "billions of years old", those trees would've withered away eons ago. for that matter, why is the same type of rock often found in separate layers? Limestone, for example, has been found at different depths, and scientists say, "well, this layer is 50 million years old, and this one is 300 million". They contain the exact same minerals, so how is that feasibly possible?
No, I am coming to the conclusion that the Earth is probably 6,000 years old (give or take a few hundred), based on scientifically provable evidence, in addition to Scripture.