alan123hk said:
If you want to measure the passage of time in this room, you have to inject some mass or matter into it before you can measure speed and time.
If there is no time in this room, then after injecting mass, time should not be produced, because the existence of time is not created by matter.
Your reasoning rests on an implicit premise that injecting mass or matter does not change any of the physical characteristics of the room.
In relativity, the technical concept corresponding to this is a "test object"--basically an object that you can use to make measurements and find out things about the spacetime geometry, but which does not itself affect the spacetime geometry. For example, if the "universe" you want to measure is flat Minkowski spacetime, and you inject some test objects into it to observe what happens to them (and thereby show, for example, that time does exist in this universe), the test objects don't change the fact that it is flat Minkowski spacetime.
In our real universe, however,
no object, strictly speaking, is an exact test object.
Every object has
some nonzero stress-energy and therefore makes
some nonzero contribution to the spacetime geometry. So it is impossible to measure anything about an empty "room" by injecting some matter or radiation into it, without
changing the spacetime geometry of the room by
some amount. The best we can do is to make that amount too small for our measurements to detect in practical cases.
And that is sufficient to ground your conclusion that, if you detect the presence of time in the "room", it was there
before you injected the matter into it to measure it, because "the presence of time" is an all or nothing thing: in technical language, either timelike curves exist in the spacetime geometry, or they don't. You can't take a manifold that doesn't have any timelike curves at all, and make it into a manifold that does by injecting a small amount of matter into it.