People did not realize what they were looking at for quite some time. Dinosaur bones found at random do not tell you much. It requires finding quite a lot of them and understanding quite a lot about comparative anatomy to stitch them into a coherent sense of what the organism was. And it requires a massive conceptual leap: that the rocks you are looking at (fossils are not bones!! they are rocks in the shape of bones) are an echo of a fantastical creature that once actually existed a long, long time ago, and in fact there was an entire fantastical world that existed a long, long time ago that looked almost nothing like ours, and somehow that entire world died. Whoa. This is entirely non-obvious even though we take it for granted today.

The traditional person to credit with figuring this out is Georges Cuvier, the eminent late-18th century paleontologist and comparative anatomist, who introduced the idea of an entire "lost world" before humans (with fantastic animals — giant sloths, giant lizards, flying giant lizards, oh my!) that did not correspond with a literal Biblical reading of Genesis, and pointed towards a much stranger geological past than people had previously really grasped. His idea that this world was destroyed in a massive catastrophe, and that the result was the notion of massive extinction, was mind-blowing for the early-19th century, and directly led to other huge conceptual leaps like Darwinism.

For a deep, scholar discussion of these issues, see Martin Rudwick's Bursting the Limits of Time, chapter 7. For a gripping popular read, I like to assign Elizabeth Kolbert's article "The Lost World," which really gets at how mind-blowing this was at the time, and how weird it is that every child today knows what a dinosaur is and has some sense of extinction relatively early on as a result.