This question is definitely one that many people end up asking after they spend a little time in science class. Thankfully, the Bible isn’t entirely silent on the subject, but we have to try our best to remember what the purpose of the Bible is—to reveal God to man and share the story of His work in the world. So, naturally, when the Bible does mention them, it’s in that context.
Perhaps you remember God’s conversation with Job, how He discusses the amazing things He’s made by His wisdom? He’s helping Job to understand who He is so that Job can understand his own place as a man before the Almighty God. In the course of that conversation which mentions many creatures and natural phenomena, God speaks for more than a chapter about two particular creatures, Leviathan and Behemoth, which sound remarkably similar to dinosaurs:
“Can you draw out Leviathan with a hook, or snare his tongue with a line which you lower?…Can you fill his skin with harpoons, or his head with fishing spears?…any hope of overcoming him is false; shall one not be overwhelmed at the sight of him?…Who can remove his outer coat? His rows of scales are his pride, shut up tightly as with a seal; one is so near another that no air can come between them…His heart is as hard as stone, even as hard as the lower millstone….He laughs at the threat of javelins. His undersides are like sharp potsherds; he spreads pointed marks in the mire” (Job 41:1-30).
This beast certainly sounds like a massive, reptilian sea creature with impenetrable scales that no man with ordinary weapons can defeat—very dinosaur-like, though the category of dinosaur itself is entirely manufactured as scientific categories generally are, and keep in mind the term “dinosaur” wasn’t coined until the 1800s during the Darwinist era (advent of evolutionary theory).
Here is another example: “Look now at the behemoth, which I made along with you…He moves his tail like a cedar; the sinews of his thighs are tightly knit. His bones are like beams of bronze. His ribs like bars of iron…Only He who made him can bring near His sword…Indeed the river may rage, yet he is not disturbed; He is confident, though the Jordan gushes into his mouth” (Job 40:15-23). Whatever this creature is, it seems very large, considering it’s tail resembles a cedar tree, and it seems undisturbed when a raging river rushes into it’s mouth. It also sounds like it can only easily be killed by God, the one who made it.
Another important thing to note is that the Word says this creature was made at the same time God made mankind, which agrees with Genesis saying that all the creatures of the earth were made on day 6, just as Adam was. That would mean the dinosaurs, too, were made at the same time and lived alongside mankind. There is nothing in the Bible—or in science, if you investigate thoroughly the dating methods and reasoning behind them—that suggests we need millions of years of death to get mankind.
A pre-mankind cycle of death itself is unbiblical, since death entered the world through Adam’s sin. And we can likely assume that some dinosaur offspring—along with other animals—could have made it onto the ark, though many of them would have been destroyed by the global flood. After all, Job seems to be dated after the time of the ark near the time of Abraham, which would put these references to dinosaurs in a post-ark timeline.