Some hypotheses are more likely than others. The Big Bang hypotheses is a very good bet to take.
We can see trees growing and take samples of their tree rings. We can see that the tree rings are thicker during wetter years and thinner during drier years. We can then extrapolate backwards to make assumptions about how old certain trees are and what kind of weather it experienced over its life. We can even look at petrified trees and extrapolate information about events that happened hundreds, or even thousands, of years ago. Clever scientists have even matched tree ring patterns across various trees to go back quite far in time.
Similar scientific methods have been used to analyze ice core samples, rock layers, etc. Processes we see going on today can be extrapolated backwards in time to make intelligent estimates about the age of certain geological structures and the earth itself.
We also can look out and see stars being formed (or at least the light that is now hitting us from those star formation events) and use that data to speculate intelligently about how our star was formed.
I am a scientist too. This artificial wall you are putting up between the study of things that happened before today and the study of things that happen after today was never stressed as having any real importance whatsoever.
Certain theories may only be supported by data gathered from controlled experiments, but other theories can be bolstered by careful analysis of existing data.
I have no doubt that you have been thoroughly trained in the modern world of speculation — what you call extrapolation.
But how many times has our understanding FLIP-FLOPPED as we learn more?
All that extrapolation CHANGES periodically. We build the house of cards that you describe, come to conclusions, and then the whole house of cards comes tumbling down and we discover that things are very different.
Everything you describe is the process of formulating hypotheses that are waiting to be tested... if they can be.
The modern world of “science” has completely lost the humility that is central to science.