First, you need to complete all the Stone Circles.
Then you need 46 pieces of silica, which you can collect from Tombs. Tomb locations appear as golden question marks on the map. Quests like The Hyena, Seven Farmers, and What's Yours Is Mine will help fill your stock.
Then take the secret passage in the Great Sphinx to Eesfet Oon-m'Aa Poo, and activate the ancient mechanism there.
Note that you could, in theory, get the armor even faster by uncovering other First Civilzation Ancient Mechanisms and NOT activating them (each pillar requires 5 silica, and is surrounded by at least five pieces), but you'd still have to come back for them later to complete each location.