For a fast Conquest, I'll prefer Aztecs with their ultra cheap uu and it's extra movement. Next is Persia with the strong immortals and then the celts with the galactic swordsman.
Even better than Immortals or Gallic Swordsmen are Mounted Warriors!
And for ultra-early military action, the Egyptian Chariot isn't bad either...
But I agree: why would you need "fast spearmen" for early quick victories? You need attackers, not defenders. The Impi may be good, if you play on Sid and need some cover for your attackers, though.