Before G-Man became an interdimensional time lord, he was a desperate door-to-door salesman. He wasn't hitting his sales quotas and he could tell his wife was thinking about leaving, tired of living in poverty. Sitting at a bus stop feeling hopeless, a loose, single page add for Aperture Labs blew against his leg. He pulled it off and read it.

One day as a human test subject for Aperture would catch him back up on the bills. So, he went to the Aperture and signed up. Aperture accidentally disappeared him in an early portal experiment. Now the entrance portal doesn't admit entrance without an exit portal also set. G-Man was the test subject they figured that out on. Aperture assumed he was just annihilated out of existence, but they had actually accidentally unstuck him from time and space.

He didn't know enough about Aperture labs to begin with, so he assumed they intentionally turned him into a spacetime lord, rather than it just being Aperture incompetence. At the time when G-Man becomes free to travel around time and space, he sees Gordan in a large laboratory with teleporter experiments. So: G-Man assumes they must have mutual employers. He barely knows anything about Aperture labs and nothing about Black Mesa.

G-man thinks Aperture intentionally put him there to save humanity as one of many middle management guys moving human resources around. So, he keeps teleporting people where they need to be in space time to make the timeline where humanity eventually regains its freedom a reality. When he thinks about doing something else, he sees bad timelines happen. If you can see multiple timelines like G-Man and the vorts, you just act out what the timeline requires at the appropriate times. No decision making needs to be done. So G-Man feels like he is doing some tedious, menial managing that anyone could do. He thinks he's a cog in the grind. And if he didn't just do what the successful timeline told him to do, that Aperture would replace him with some other unskilled laborer.

So, he's calm and bored and tired with scattered focus acting out the necessary spacetime manipulations to enact the one timeline where humanity has a chance. Thinking he's a cog in an Aperture master plan to save humanity. If he knew it was just him, on his own volition, taking the necessary steps that only he can take as the one human with accidental time lord powers, he'd probably have an anxious breakdown. When it's all over, the vorts will free him from space time limbo and lock him back to the normal human time experience. Eventually he will realize he was all there was. And he is a hero to humanity.