In Genesis 14:7 we see this verse.
Then they turned back and went to En Mishpat (that is, Kadesh), and they conquered the whole territory of the Amalekites, as well as the Amorites who were living in Hazezon Tamar.
This implies that the Amalekites existed before Esau was born. However, we are told in Genesis 36:12 that the Amalekites are a descendant of Esau.
Timna was a concubine of Esau’s son Eliphaz and she bore Amalek to Eliphaz.