[jhanschoo]

Not knowing the configuration of a TM at time t without running it (or similarly involved computation) doesn't mean that we cannot divide the space of TMs into classes.

One class has to each TM an associated mathematical function mapping inputs to nonnegative integers that tells you the exact integral time at which the TM transitions to the halting state. This is the class of decidable TMs.

The other class contains every TM not in the first class. For this class, any choice of such a function is provably wrong for some input. This is the class of undecicdable TMs.

Both classes are nonempty, and their existence is just about as well-defined as many other common mathematical objects. It is just not possible to provide a "nice" alternative characterization which TMs fall under which class.