Half-Life narrative is always at its best when it isn't beating you over the head with exposition but instead scattering observational and passive narrative for the player to digest however they wish. The GMAN never needed an explanation, not in the sense of a lore dump or big reveal. Even in the context of deus ex machina, the Gman, Combine, Vortigaunts, and so on are exciting to speculate about. It's successful science fiction in that regard, baiting just enough to sew seeds of intrigue and idea, but not enough to outright explain characters and events.
The Combine Empire being so much grander fits their motif; it's implied their a dominant interdimensional multi-species empire, ruled by telepathic grubs, that conquer and subjugate species into their order. They're particularly adept at biomechanical technology, but limited with portal science. This strength and limitation is a cornerstone of their conquest operations; surprise attack a targeted world and while cut off from their homeworld due to one way portal tech subjugate the local species. Episode 1 and 2 revolve around this arc, the Combine having met frantic resistance on Earth and seeking a way to reconnect with the homeworld for reinforcements. Episode 3 culminating with the Combine sourcing mankind's greatest portal technology, and Gordon witnessing the true scope of the Empire, is a perfect end to the three part arc to lead into a third major act.
Similar with the GMAN. He's deus ex machina incarnate, but we don't need an exposition dump on his exact origins and purpose. We can piece together enough that can be lightly expanded in other episodes too; he's an enigmatic creature (or creatures, or idea) masquerading a human being, seemingly involved with investment in and acquisition of assets pertaining to conflicts between other species. Like an interdimensional arms dealer.
