Well, there's at least one definition that's pretty noncontroversial, if not terribly satisfying or precise: it's not a JIT if you compile well in advance of any indication the program needs to be run.

Whether that lazy-compilation strategy is fine-grained or not isn't clearcut, I believe. I think if you distribute a C program with a bash bootstrapper calling plain old gcc to compile and run the C code only when needed, even gcc might be considered a (coarse-grained, rather rudimentary) JIT in that context.

Like TCCBoot? https://bellard.org/tcc/tccboot.html