How scientist found age of universe as 13.8 billion years and age of Milky Way as 13.51 Billion years? Is there any proof?
It's impossible to mathematically "prove" those things in the way that mathematicians prove axioms. Instead, physicists compare the predictions of a model of the universe with experimental observations made on it in order to verify the correctness of that model; those observations having certain statistical limits on their stated accuracy. They also use that data to refine their models so as to include more physics in them and thereby increase their predictive power and accuracy.
Finally, physicists make comparisons between different models to determine whether or not their own model is consistent with those others, within the accuracy limits mentioned above. This process is used to rule in or rule out the validity of the model in question.
None of these processes rely on mathematical proof as such.