Dinosaurs lived on the far side of the galaxy. That is, the Sun orbits around the galaxy’s center, and it’s a long trip, about 250 million years. Dinosaurs — in particular, the big Jurassic critters like tyrannosaurs — lived about 166 to 66 million years ago, so they lived in a different neighborhood of the galaxy.
Here’s the cool part. Because the stars move around in relationship to each other as well as in their orbits, the neighboring stars are different over time. In that way, space travel is possible to distant stars if the travelers are patient and have generation ships (presuming these creatures have generations like human beings). They can hop from star to star, sometimes pausing to rest, and meanwhile the stars will take them to new parts of the galaxy.
So, it just might be vaguely possible that Earth was visited over on the far side of the galaxy by slow travelers, and they took Earth faunae with them as they continued on, bringing them to new homes. Dinosaurs in space! Land of the Lost without a dimensional portal!
Or perhaps they took a different Jurassic lineage, and there’s a Planet of the Turtles out there somewhere.