Here's a thought I had on how Doomsday could exist before Cadmus:
Sometime after Legacy (STAS) and before Secret Origins (JL), a secret unnamed government program was setup to create a weapon to fight Superman if he ever went rogue again. I'm going to call it Project Doomsday, since if Superman ever truly went rogue it would be Doomsday wouldn't it? Using a sample of his DNA, this program created Doomsday, but as Dr. Milo (man I feel creepy for just typing that idiot's name. oh well at least he's gone YAY!) explained the Doomsday monster was too powerful and was sent off into space on the rocket then when the Justice Lords arrived, and the events mentioned above happened, the program was then placed under Cadmus control probably along with all super powered related experiments i.e. the institute that turned Volcana into a weapon, the foundation that had the 1st Royal Flush Gang before Joker arrived, etc. I'm even going to go further and say The Terrific Trio in Batman Beyond was part of this Government-sponsored super power program because to counter the perceived threat of the Justice League, the military needed a counter force.
So this is how I think Doomsday could have existed before Cadmus, any thoughts?