The word "day" can be used to mean "age", "time period", or "era". A quick search on the Hebrew word used in Genesis for "day" will give you these other usages. Also Jesus himself used "day in this way:
John 8:56 Your father Abraham rejoiced to see My day, and he saw it and was glad.”
So, let's say that "day" in Genesis, as in "the evening and the morning were the first day", means time period. Thru Peter we learn that a day with the Lord is as 1000 years. I believe "is as (or like) a thousand years" just means a long period of time. Possibly as many as 1 million.
Now for the "evening and the morning were...". We all have heard the phrase "Dawn of the _____", whether Dawn of the Iron Age, or Dawn of the Age of Dinosaurs. "Morning" here in Genesis means morning or break of day or dawn.
"Evening" means evening or night or sunset. We all have heard the usage of the "sun setting on _______", whether on someones life, or an empire, or a time period.
"So the evening and the morning were the second day." could easily understood as "So the sunset of that age and the dawn of the next age ends the second age(era)."
In this way of thinking, the dinosaurs lived in the 5th age or era.
Genesis 1:20 Then God said, “Let the waters abound with an abundance of living creatures, and let birds fly above the earth across the face of the firmament of the heavens.” 21 So God created great sea creatures and every living thing that moves, with which the waters abounded, according to their kind, and every winged bird according to its kind. And God saw that it was good. 22 And God blessed them, saying, “Be fruitful and multiply, and fill the waters in the seas, and let birds multiply on the earth.” 23 So the evening and the morning were the fifth day.
God says "creatures" and "birds". Scientists are now telling us that dinosaurs are actually the ancestors of birds. The Bible had this recorded long ago. Dinosaurs are these unspecified creatures and birds of verse 20. Animals that we know today were created on the sixth day(Age) in verse 24 and 25.
This is where you find dinosaurs in the Bible.