Earthquakes PGA/PGV in time?
No. However, you can look at backprojection results which show where the energy is coming from. It gives you some idea about how the earthquake evolved in time, e.g., see here (click play to see the video).

The only other way to get what you want is to use observations from dense arrays. E.g., see here, but this is only possible in certain regions.

EDIT (answer to your comment below): Codes like SPECFEM3D are good for simulating low frequency ground motion (e.g., 0.1-1Hz). High frequency (1-10Hz) ground motion, that affects smaller structures like 1-2 story houses or even mid-rise buildings is very difficult to simulate (you need a very accurate, very high resolution, velocity model with the right soil/geotechnical layer etc., a highly accurate source model with the 'right' slip distribution, rise time, rupture velocity etc., and finally, a very large supercomputer). You're better off using GMPE's like USGS but that will not tell you how things evolve in time.

Bottomline is that statistics of high frequency ground motion are rather well understood (scales with distance) but not for lower frequencies where effects like rupture directivity/velocity, path/basin effect etc. become even more important.

Finally, Okada's elastostatic solutions are for calculating the final displacement field and doesn't have time component, i.e., you can simulate the final slip but not how it evolves with time which is an elastodynamic problem. Also, the final displacement field alone doesn't tell you anything about PGA/PGV.