After a Phantom Mass came from the previous universe and threatened to consume all of reality, Madrid tried to stop it but the Infinity Engine needed to be calibrated from the moment it enter chronospace. She hd to acquire both the Beta-Engine and the Dynasty's Fortress ship and the calibration itself required solving a seven-hundred-quantum-formula, fuzzy-matrix, morphing "puzzle" in twenty minutes. However, Madrid was thrown free of this reality and back to the dying previous one. Since then, she taken the new identity of "Ancient Madrid", and while waiting for to return to the current timeline, she grew in greatly in power and began working on Positive Infinity, one half of the Infinity Engine.
However, she needed someone who could work on Negative Infinity, the other half of the Infinity Engine. So she used her powers to manipulate the events that led to Dreadwing getting control of the Time Raft, the events the led to him getting thrown into chronospace for eons and eventually ending up at the beginning of time and fusing with Dr. Peachbody. The fusion with Dreadwing's magic and Peachbody's scientific skill, also the belief that it was Gina that put him there, gave Dreadwing the skillset and the hateful drive to spend the millions of years to create Negative Infinity.
The ultimate end goal of Ancient Gina is to give the Infinity Engine to her younger self so that she can save the existence. Dreadwing's ultimate end goal is to kill Ancient Gina after she saves the universe and take control of all of time and space.