If you mean written sources, the oldest attested language is Sumerian. I recommend you start there. Akkadian and Hittite are also very old. Broadly, the oldest known languages come from the Middle East (including Egypt) and many are Semitic (Hebrew is very old, and so is Phoenician). Outside of that region, Old Chinese goes back thousands of years, and in Europe, I believe the oldest known language is Ancient Greek. This would be a good question for /r/linguistics.

A history sub will focus more on written evidence (tablets, scrolls, etc), but if you're looking for earlier evidence of speech, considering x-posting to /r/AskAnthropology