It seems to me that the one and only thing we know about Eggman is that he actually knew his grandfather, that he admired him when he was still a child. Much like Sonic's origin, Eggman's origin is intentionally unclear, if not completely unknown. What do you think Eggman's life was like between his birth and the events of Sonic 1 (or perhaps, his "very first" meeting with Sonic)?
Eggman strikes me as a former businessman. Varying elements of his character have stated he either wants to take over the world or just build "the ultimate amusement park." Sometimes its a city.
Generally, he seeks power. Actual power. Fuel. He is not altruistic with his fuel consumption, either. He's 100% willing and able to subjugate living beings as a power source.
And where does he get the materials? Why isn't he in more trouble with the authorities? If they're willing to arrest and incarcerate Sonic the Hedgehog, the guy who routinely defeats Dr. Eggman, why aren't they going to war against Eggman himself?
Because Eggman is rich, powerful and connected. Where do you think GUN got its robots?
Is it any surprise that these don't look that far off from an E-Series robot?
The toes on the feet, the vents on the chest, a domed head...
I imagine the incident on the ARK did not go as planned. The government wanted to cover up Maria's death (and whatever other deaths occurred), as well as cover up what was going on up there at all -- research into immortality and such. They didn't want news of Shadow, or Biolizard, or anything getting out to anyone.
Gerald refused to keep quiet. He descended into madness and planned the extinction of planet earth. Gerald was executed but obviously had a family. That family would need to be paid for their silence. Overnight, the Robotniks became multi-millionaires. Whatever they wanted, they got.
This created the perfect environment for Eggman to become a spoiled brat with infinite resources. Worst of all, he idolized his grandfather, the deadly martyr. I'm sure there were those within GUN that kept very close tabs on Eggman's progress, and they may have even stepped in at some point, hoping to persuade the boy towards a path of "good" at an early age.
Eggman eventually reached a point where he could support himself with his robotics work. Using his family fortune, it blossomed into a massive business. Military contracts were a matter of course.
Eventually he started reaching people who were afraid of the limits he was testing. He was developing dangerous weapons of mass destruction. Delving into the secrets of consciousness. Even dark new sources of energy. He was going too far, and starting to echo his grandfather a little too well.
(Imagine Eggman laying out plans for his space station research facility and somebody from GUN tugging at their collar like "we know how this ends")
But he grew up in a world where nobody had ever told him "no" before. He saw these limits as weakness. A lack of ambition. Every attempt to go around the problem just caused more problems. People started turning their backs on him for being an increasingly dangerous radical breaking the laws of nature.
Eggman came to the ultimate conclusion: if the city won't approve, if the nation won't approve, then go somewhere that will. Even if that means having to build it yourself. Nobody will ever tell him no. And one day, they'll thank him for what he's going to do for this world.
And who's going to stop him? The government running ten year old versions of robots he designed for them?
All he needs now is the location and a power source...