First, the universe as we know it is about 13.7 billion years old. It is currently expanding and has been expanding for the last 13.7 billion years.<quoted text>You are the expert in math and physics. My belief is that the universe came into existence very quickly and it expanded or branched out in full form. You apparently believe it took very great amounts of time for the cosmos to form, is this correct?
Second, it was much hotter and denser in the past (as a result of being more compressed).
Third, it did not expand from a central point. Instead, space itself is expanding.
Fourth, the initial stages of formation of simple atomic nuceli (hydrogen, helium, lithium) was very fast and happened within a few minutes of the start of the expansion. It wasn't until about 1-300,000 years later that the universe cooled enough for stable atoms (nuclei with electrons) to form. Stars and galaxies were much later.
Fifth, the heavier elements, like those required for life, did not form until the first generation of stars exploded (allowing fusion to make those elements).
Our sun is a third generation star and didn't form until about 9 billion years after the start of the universal expansion. The earth formed about the same time as the sun.
So, to answer your question, some aspects happened very quickly (formation of nuclei), while other processes took more time (stars, life, etc). In any case, the current expansion phase is about 13.7 billion years old and our earth is about 4.5 billion years old. Life has been around for at least 3.8 billion years, but complex life (multi-cellular) for only 1 billion years.
And yes, this is what the evidence we have dictates. There is no way to reasonably interpret the evidence as saying the earth is only thousands of years old.