In gtr there is proper time, which we can describe as a fundamental temporal variable. It is not a single variable, but there is proper time associated with any material body. I don't think anyone who understands gtr believes that proper time can be reduced to a single temporal dimension or variable, but one may think that this idea of 'many fingered time', i.e. the multiplicity of proper times associated with material bodies, is replaces the classical idea of time as a fundamental temporal dimension. As for whether the notion of proper time will survive the quantisation of space-time, it is quite straightforward to formulate relativistic quantum mechanics using proper time, and we may consider that since proper time can be used in both qm and gtr, it will survive the unification of the two. On the other hand the orthodox interpretation of quantum mechanics is that observables do not exist with precise values except when a system is in an eigenstate of the observable, and since objects are not necessarily in eigenstates of position it is not possible to treat 3D space as a fundamental concept.
Systems consists of collections of interacting particles.
The size of a system is determined, not by the existence of a prior space which can be spanned, but by the time taken for information to navigate the system. Any positional information for any particle in the system, relative to another, is determined in practice from the proper time of the second particle.