Actually, the Spartan II's were trained from age 6. The Spartan III's were orphaned children whose parents were killed by the Covenant; they volunteered, and a lot of them were even younger. And the Spartan IV's include soldiers from every branch of the UNSC military who volunteered, including Spartan III's who were willing to be integrated into the program. At least, this is what I've read in Halo: Glasslands.