[AnonNo15]

None of the above needs to happen overnight. Who knows what humanity will be capable of in 1000 years?

Furthermore, in a strict sense my question would be 'Is it possible to extract additional information with any degree of certainty about the past state of some region of the universe, using simulation algorithms and partial information about past states of this region?'

This assumption doesn't need to go to the atomic level on the first try. If you can replicate distribution of mass on the scale of galaxy clusters as compared to the present day using the above approach, it would certainly prompt further research in this area.