The Ancient Egyptians were called Kemites. The word Chemistry is derived from this name. They way higher education was done then was a roughly 40 year program that was split between mathematics, science and magic. No outsiders ever completed the program but a few notable Greeks did many years (i think maximum about 17 yrs but i don't remember who it was offhand) and brought what they learned about about science and math back to Greece with them but never really made it to the magic part. This is all pretty well documented.
The Kemites didn't have any type of established system of philosophy though so their approach to science was strictly practical. Medicine and chemistry was a practical science for them whereas something like Astronomy was nearly useless for them because they never really needed to learn to navigate by the stars. Also, there was no need for a Kemite to define things like "gravity" because it was common sense that if you drop something it's going to fall.
I'm using the Ancient Egyptians as an example just because I'm most familiar with them but really, science is a very broad term and it would be easy to make the case that mankind has been using science since the beginning of our existence but even thinking in a slightly more strict modern sense there were plenty of ancient cultures that used, studied and recorded science. Keep in mind you're talking about medicine, physics, geology, botany, chemistry, biology, mathematics and so forth.