>>14069125A geodesic is the smallest metric between two defined points in four dimensions. In general relativity that's three space dimensions and one time dimension. The time dimension exhibits itself as the photoelectric effect relating to microstates which provide intrinsic properties like temperature and charge. That only changes when it's the easiest thing to do. The energy required is on the level of neutron stars and black holes colliding. Instead of moving, it's easier to tell the entire universe to adjust their gravitational fields and change the amount of particles in those neutron stars or black holes.
Geodesics and relative time is not required to explain inertia. Inertia originates from the discovery there is no absolute position and velocity. Velocity only makes sense between two bodies. If velocity for one is to change, another thing needs to change or have the ability to absorb it without changing.
Something exists. It has enough to resist a series of interactions. It also has enough to interact with other things. That's what matter and mass is.