Some observations: the masses of celestial objects are all moving away from each other, as if expanding. If they are moving away from each other, it's a pretty good assumption that, if we were to rewind that, at one point, they were all together.

Measuring the velocity with which they are moving is easy enough. So, coming up with a model for rewinding that (and how long that would take) is actually not the most complicated thing in the world. If we were to "rewind" it, it would take ~14 billion years. Of course, there may be some variables that effect that age, but most of the biggest ones (gravity, expansion, etc) are fairly easily observed and accounted for. So it is unlikely based off current observations that we are trillions of years off. Millions perhaps, but that's fairly small.