I don't pretend to know the age of the Earth. However, I can safely count the years from Adam. Personally, I lean to a very literal interpretation of Creation.
How do I "overlook" what scientists and my own research has often told me about the age of the planet and the universe?
It isn't that I "overlook" it at all. Rather, I trust in the unlimited, omnipotent nature of God.
Remember: Nothing is outside of God's control. God can make a single second last for trillions of years. God can speed up the speed of light. In fact, God is not confined to "time" or "space" at all.
God could have created a "mature" universe in much the same way that a painter can paint a building that is "weathered."
As for the dinosaurs: A fossil is not a record of death...but a record of catastrophe. If an elephant dies in some African field, its bones will eventually whither away by the elements. This is not true of dinosaurs. The existence of their bones represent a catastrophe that preserved the bones. The Bible offers an explanation or world-wide catastrophe through the flood.
Also, it can be argued that dinosaurs DO appear in the Bible. Not only do we read of the leviathan and behemoth, but we also read about a DRAGON.
Satan is often described as an "ancient dragon." This might allude to the time in the Garden where Eve was beguiled through a "serpent." For his punishment, the serpent was cursed to crawl upon its belly. So, what did a serpent look like BEFORE that punishment? After all, the serpent was cursed above all "beasts of the field."
In Revelation, we read of Satan being considered the "dragon." In fact, in Revelation 12:9, we see a connection between a dragon and a serpent:
And the great DRAGON was cast out, THAT OLD SERPENT, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him. - Revelation 12:9
Now, there are many the theories about this world presented by both scientists and theologians. My faith in God causes me to give up my doubt to him. I KNOW that God exists -- and I have more faith in God than even what I think that I know of science.
Like I said, God is omnipotent and omniscient. He can stretch time so that a second lasts for millions, billions or even trillions of years. Eternity is just that -- ETERNAL. God is present in Eternity. He allowed John to be "caught up" so that he saw things that would not take place for thousands of years. How? John likely had a glimpse from the scope of eternity.
There is an old saying that we used to have on a refrigerator magnet growing up: "DON'T WORRY ABOUT TOMORROW -- GOD IS ALREADY THERE." The same is true of yesterday, today and forever. God is there. His mind cannot be understood by the wisest of wise men. Therefore, I endeavor to trust Him even when what I learn might tell me something entirely different.
I hope that this makes some sense. We can rest assured that God created this world and all that is in it. How did he do it? I have no idea.