Final answer:
Dinosaurs were very much alive during the Early Jurassic, which was their golden age. It wasn't until about 65 million years ago, at the end of the Mesozoic Era, that they went extinct due to a mass extinction event.
Step-by-step explanation:
By the Early Jurassic, the mass extinction that ended the Triassic had led to the extinction of numerous species, allowing for the dinosaurs to flourish. Contrary to the implication in the question, dinosaurs were not extinct during the Early Jurassic. In fact, the Jurassic Period, which lasted from about 200 to 145 million years ago, was the golden age of dinosaurs. During this time, the dinosaurs dominated the land ecosystems as they adapted into a variety of forms and filled many ecological niches.
The dinosaurs were a diverse group of terrestrial reptiles. Types of dinosaurs during the Jurassic included the Saurischia ("lizard-hipped") dinosaurs and their counterparts, all adapting to their environments with varying diets and behaviors. This period saw the appearance of some of the most iconic dinosaurs, as well as significant evolutionary developments such as the rise of early birds from reptilian ancestors and the evolution of all major groups of mammals, although individual mammals remained small during this era.
It was not until the end of the Mesozoic, specifically the Cretaceous-Paleogene extinction event about 65 million years ago, that the dinosaurs went extinct. This event marked the fall of these once-dominant creatures, paving the way for mammals to eventually become the dominant terrestrial animals.