Some datasheets might note it explicity as a class. It'd be easy to tell if it was one of the switching types (D,E,F), one of the linear types (A,B, AB, C), or one of the hybrid types (G and H). They'll probably tell you if it's switching or hybrid right off the bat. They might not say if it's linear though since it might be so common as to be a given if nothing else is said. The actual class might not be specified. But you can find out or at least narrow it down by looking at how the amp works.
You can go about it by picking the performance and efficiency you need whch indirectly refers to the class, or picking the class which indirectly refers to the performance and efficiency. So class is not always explicity given.
Just note that switching types are more complicated to design for becayse more work is left to the user as it requies external components. That's usually the case with switching anythign vs linear anything.