It's not 100% complete, but close enough.
After the victory by the forces of the United Federation, Kingdom of Acorn and it's allies over the Eggman Empire in Mobian Alert, the Egg Emperor found himself cornered in his throne room by his archenemy. While Shadow the Hedgehog and other agents had helped Sonic take down the last bastion of the Eggman Empire, it was decided that it was Sonic's right to be the one to take down the fat man himself.
In the ensuing battle, the Egg Dome was completely destroyed thanks to the carnage within. While Julian Ivo Robotnik had been defeated, he refused to surrender. Rather, he fled deeper into his fortress as it fell apart, with his blue nemesis in pursuit. However, the blue hedgehog had decided to toy with his archenemy, following more slowly than he could.
This mistake would prove foolish. Eggman was eventually cornered in a labratory, where he had placed himself in a podlike device. While Sonic assured the good doctor that he would defeat any robot or chase any escape pod, the Doctor replied with his usual evil laughter, stating, "I am escaping, rodent, but to another time and another place, somewhere not even you can follow me!"
The hero was surprised to see Eggman's pod vanish in a flash of light...
---
The Doctor rematerialised several years beforehand, at GUN Headquarters. The day and time he had chosen was the same day that the infamous Shadow the Hedgehog had joined the military organisation, thus providing GUN with huge amounts of information on the Eggman Empire - Shadow having been a former agent of the Doctor. With a single touch, those who would have met with Shadow found themselves erased, and thus a meeting was arranged between the black hedgehog and the mad scientist instead.
The ultimate lifeform retained his usual cool and collected appearance despite the change of events, and the Doctor began to do his work. Unable to erase Shadow as well - having tried and failed, this was reasoned to how Shadow existed 'outside' of time in a sense, and thus was immune to being erased, just like he was immune to roboticisation - the Doctor tried to reason with him.
Dr. Eggman claimed that it was strange that Shadow was planning to throw his lot in with humans, or GUN specifically. It was the humans, via GUN, who had killed everyone who Shadow had ever cared about, and the few who treated him as a person rather than a weapon or tool. An organisation would always stay an organisation, and what was to prevent Shadow from becoming the same cold-blooded murderer that previous GUN agents had?
After a bit of logic, the lifeform was dissuaded from signing up after all. As Eggman vanished, he let out a deep bellow of evil laughter, knowing he was sure to have damaged GUN's war effort...
---
Returning to the exact time and place he had left, Eggman found his base intact. He checked his data screens, and saw that the majority of the Eggman Empire was still stable and under his control, even while parts of it had collapsed as a natural part of the stress of war.
When asking his computer to give him a full update on the status of all provinces, the list showed their "damage" meters, as a measure of how much destruction had been caused by the enemy countries. Eggman asked where the "Eastern provinces" were on the list.
The computer responded that the Eggman Empire signed over the majority of it's eastern territories to Red Claw after humiliation in the Dragon Kingdom by the same group.
Naturally, Eggman asked what "Red Claw" was. He was answered by a large history lesson on how it was an organisation founded several years ago in the barren tundra of the former Siberia. It developed under a powerful leadership with access to the region's natural resources, until it became a regional power that humbled the Eggman Empire.
...What was more shocking was it's leader.
Shadow the Hedgehog.
Eggman soon received an incoming message. Upon agreeing to view it, he found it was a video conversation with said hedgehog, dressed in an imperial military robe. The hedgehog chuckled, mentioning how Eggman had done the world a favor by preventing Shadow's joining of GUN. Because of staying rogue, Shadow had realised his full potential and founded a cosmopolitan superpower accepting of all beings, human, Mobian or robotic. Shadow concluded the meeting by saying, "You may have been able to alter the past and change our present, but do you know what the future will hold, Doctor?"
With the conversation ended, Eggman pulled on his moustache, due to a lack of head hair to pull on. His attempts to weaken GUN had succeeded enormously, but at the expense of much of his empire and the formation of a technologically-advanced, well-trained foe on his eastern borders.
The Doctor immediately rushed to draw up plans... hoping he could find some way to turn this to his advantage...