RobA has answered that quite well, and if you just keep asking it in different forms, eventually you will be taught all of astrophysics-- that's a tall order.
This seems to be your fundamental issue, I dare say. But anyone is free to "believe" whatever they choose. Contrary to popular belief, physics theories are not intended to create belief. They are intended to unify, organize, and predict, observations. Period, that's what they do. What you believe about them, in terms of their fundamental ontology (the primitive elements that the theories assume exist), is up to you.

Indeed, there is essentially no major physics theory that has not seen substantial reconstruction of its fundamental ontologies over the course of science's advances. Belief in the ontology of our theories is a luxury that we all avail ourselves of, essentially for convenience and satisfaction, but it is no required aspect of the theory. The real question is not why would you choose to believe it, but rather, why would you choose to believe something else?
Some of the age measures that the Big Bang theory unifies, when one
appends dark matter and dark energy (required to unify other observed effects) include:
--the dynamical age imprinted in the Hubble flow
--the age of the oldest stars, based on evolutionary models
--the amount of heavier elements produced in stellar nucleosynthesis
--the history of galaxy and supermassive black hole formation
In short, the age of everything that we have seen is happening on grand scales in the universe.
We never know how "far out" anything is. Distance is also a theoretical construct, used to unify and organize another whole class of observations. We take local observations of distance we use in our everyday lives, and extend them out into space using the "ladder of distance scales". This "ladder" is another example of how we unify concepts that work in the laboratory with concepts that work as consistently in the rest of the cosmos.

Again, believe what you will, but the unifying power of the approach of science is well documented. Sometimes it leads to principles and technology we rely on every day, and other times it is just science applied to things that are far away and have little direct effect on us.

__________________
Logic is the grammar of truth.

Meaning and absolute certainty are incompatible, and profound meaning and absolute certainty are profoundly incompatible.

The only thing intelligence is capable of is recognizing itself.