Many young people have walked away from the faith because someone told them they had to choose between Genesis and the fossil record. That is a false choice the historic Church never required.
Where are dinosaurs in the Bible?
By name — nowhere. The word "dinosaur" was coined in 1842 by Sir Richard Owen. Behemoth (Job 40) and Leviathan (Job 41) are poetic portraits of awesome creatures; some Christians read them as dinosaurs, others as mythologized hippopotamus and crocodile, others as symbolic of cosmic chaos. The Bible isn't trying to give you taxonomy.
Faithful Christian options on origins
- Young Earth Creationism — universe ~6,000–10,000 years old; dinosaurs lived alongside humans; fossil record from the Flood. (Answers in Genesis, ICR.)
- Old Earth Creationism — 13.8 billion-year universe consistent with Genesis 1's "days" as eras or framework. (Reasons to Believe — Hugh Ross.)
- Evolutionary Creation — God created through an evolutionary process; Adam and Eve as the first humans uniquely endowed with God's image. (BioLogos — Francis Collins, who led the Human Genome Project.)
Orthodoxy doesn't dogmatize any one of these. What it confesses: God created everything, ex nihilo, freely, out of love; creation is good; humans bear God's image uniquely; sin and death are intruders.
The Orthodox lens
St. Basil the Great preached his famous Hexaemeron on the days of creation in 378 A.D. — full of fascination for marine biology, animal behavior, and astronomy. The Fathers were not afraid of natural history. St. Augustine warned against Christians making science look foolish by insisting on naive readings of Genesis. The wisdom is ancient.
A pastoral word
If a museum visit shook your faith, take a breath. The God who made T. rex is the same God who became a child in Bethlehem. Studying his creation is itself a form of worship. "The heavens declare the glory of God" (Ps. 19:1) — fossils included.