That's an excellent question, Robin. The Big Bang Theory is the best explanation we have, so far, to explain what is observed and what is measureable. It is not a perfect concept and is constantly being challenged and refined. It greatest strength is in its ability to predict certain things about the universe. For instance when the concept was first developed it suggested that the universe should contain approximately 75% hydrogen, 24% helium, and 1% other scattered elements. Since then we have found that those proportions are exactally what we find throughout the observable universe. Another prediction the theory made was that due to the high temperatures which existed in the small, hot early universe, we should still be able to find some pervasive 'after-glow' remaining from the BB itself. That after-glow was sought for many years without success until it was found, by accident, while technicians were trying to eliminate a persistant white-noise sort of interference which nagged early micro-wave radio reception. It was determined that the noise polluting those micro-wave broadcasts came from every direction was at almost exactlly the right frequency for the ancient light from the dawn of the universe. Later research has actually mapped that micro-wave background radiation across the entire observable universe.
The strength of any scientific theory comes from its ability to withstand testing. As soon as a scientist publishes a theory, other scientists start trying to disprove it. A true theory must make predictions and it must be testable, to qualify as a 'Theory'. Einstein's Theories of Special and General Relativity are still being put to the test almost 100 years after they were first published. So far, they have survived every test, but no scientist will claim that they have been "proven", only reinforced. It's the same way with the Big Bang.
A funny thing about Einstein and the BB -- he didn't like the idea. He believed in the concept of a 'Steady State' universe. An infinite and eternal, unchanging universe. But, while working with his General Relativity equations he found that the equations said the universe should be expanding. The only way he could make the numbers work was to add, what he called, a "Cosmological Constant". This troubled him greatly. He called the Cosmological Constant his greatest blunder. Much later, the astronomer Edwin Hubble found that many of the 'spiral nebulae' seen through telescopes were actually individual galaxies, and that they were all receeding from us, and from each other, at a rate which matched Einstein's Cosmological Constant. So there are checks and ballances within astronomy, physics, and cosmology. Nothing is ever taken at face value.



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