When you study hodgepodge that is the English language, you can look back through the various words to find an origin in another, older, language.
For instance, in writing this post, I've learned that "hodgepodge" came from the 15th century term hotchpot which was a type of stew. And THAT came from a 13th century word: hotchpot. And from there I could trace it back a bit further to Middle English and then either old Dutch or Germanic roots.
Everything seems to have Old English or Greek or Latin roots. But how far back can I really go? Suppose I was a Roman language historian in 5th century BC and I wanted to know the origin of the Latin and the other languages around me. How far back could I go? How far back can we go today? Who was the first person to point at a big cooking bowl and declare that to be a pot and how did they come up with that word?
We can go back to Proto-Indo-European, the ancestor of most of today's European languages, as well as Persian and the languages of India. This language is entirely reconstructed, based on similarities of known languages like Latin, Greek, Sanskrit, Gothic, and others. This was probably spoken by people living in the steppes north of the Caspian Sea around 5000 BC, although this is debated, with some scholars pushing the date back to Anatolia (modern-day Turkey) around 8000 BC.
There are other language families, such as Finno-Ugric, that we can reconstruct to similar ages, but it is difficult to go back further than that. Some people try to take the known language families and reconstruct an earlier parent of them called "Nostratic," but it is difficult to be nearly as certain about this as we are about Indo-European.
A good book for non-specialists on this is J. P. Mallory, In Search of Indo-Europeans. The wikipedia entries on Indo-European culture and languages are also very good and have further references.