What difference does it make if there were dinosaurs or not?
The world was created old, complete with fossils and ancient rocks.
This is absolutely certain:
A. The Torah says that there were rivers coming from gan eden, and a river takes a great while to be carved out (proof: we don’t see rivers spontaneously appearing, rather slowly getting deeper).
B. Adam HaRishon and Chavah was able to talk, and had the intelligence of at least a twenty-year-people (they were clearly held responsible for their actions), despite being only a few hours old.
C. Gan Eden was full of both fully-grown fruit-bearing trees, and trees take years to grow (this is indisputable)
Additionally, the theory of relativity states that time is not constant, and depends on the speed of the object in space. Because we don’t know what the flow of time was back then, scientists cannot know how old the world is historically, because the flow of time could have been (and probably was,) warped.
Thus, carbon-dating and fossils (even if the methods are 100% accurate) are then no proof against the Torah’s narrative. The Torah painstakingly records the precise history of the world historically. The scientists analyze the world and find its chronological age.
No contradiction.
(Of course, the above cannot be scientifically proven, so bechirah is preserved)