YEC/OEC question about dinosaur tissue?

Lately I have seen a lot of evidence for Old Earth Creationism as opposed to Young Earth Creationism, but I have been taught YEC since I was a child. This leaves me with some questions about previous evidence I have heard. For example, I remember a video that said that scientists found soft dinosaur tissue with some DNA that would have broken down by now if dinosaurs lives 65 million years ago. What should I make of this? I consider myself an Age-Agnostic Creationist for now, but I would like to choose a side in accordance with the evidence.