As a matter of fact, science can so observe some aspects of the distant past. Light has a speed. Light from far away started long ago.
In this way, we know of some very early times in the existence of the universe, for the light from that early time is now the cosmic microwave background radiation.
Light from distant galaxies comes to us from 1 or 2 or 5 or 10 billion years ago.
We can also gain information about distant times from geology. From DNA, which evolves in its “junk” sections at a fairly constant rate. From radioactive elements, which decay at absolutely constant rates, with the exception of what happens in reactors. And yes, from tree rings and ice layers.
All these things give us observations of the past.
You lack understanding of basic cosmology.
When God expanded the universe (as a 'white hole') he expanded time along with it. The simpleton's assumption that light from distant sources took a long time getting here disregards General Relativity completely. Read Dr. D. Russel Humphreys' "Starlight and Time" (or view the video if you're too poor a reader) to get an understanding of what really happened, and why the universe appears vastly older than it is to the uninformed.
For those that have a grasp of math, the book contains the equations that prove the model beyond the level to which the 'big bang' is cobbled together. That the universe has expanded is a known fact, and so is the expansion of time. Get educated, and don't be propagandized by those anxious to take advantage of your ignorance.