I know what a Green Man looks like; I researched it before making that post, in part to check the character's background and in part to see whether it was part of a species rather than an individual. It wasn't, but that's only tangentially related to the affairs here, since recruiting duplicates of mythological figures isn't out of the question. I remember that July recruited a version of Asclepius for the Medical Department one time, so there's precedent for it. Maybe Montgomery Osbert or one of the other first-generation Agents could have found a Green Man in the early days due to a particularly confusing typo or poorly phrased simile. (By the way, that version of the Green Man that you linked didn't have limbs or fronds, so it couldn't be the Greenman.)

I don't think that anything is "obvious" with this little to go off of, though. Anything can be construed as "obvious" if someone makes logical jumps in the right places. We don't have a lot of description to work with here, so plenty of potential identities for the currently mysterious Greenman could seem obvious to different people. To you, that bronze man-faced bloom form of the Green Man is the clearest interpretation. To me, the mythological identity is still unlikely, especially if the supposed point of clarity for that explanation is that the Greenman would have been created as an extension of the "plant theme". It seems strange to me that the officials of the PPC would follow the pattern of "sunflower, lichen, processed wood, daisy, mythological representation of the spirit of the earth". The last entry just doesn't seem to match the pattern set by the first few. I'm not saying it's impossible; if I thought that, I wouldn't have put it up for consideration at all, but it's not a clear-cut solution.
Also, since the Greenman was never mentioned or fully described anywhere else, he is only being defined now, using the understanding of PPC continuity that is currently in use. Whatever we decide here would need to be compatible with that. I'm not trying to go against the original writing here, and any authorial intent that someone manages to dig up will trump anything else we decide, but I sincerely doubt we'll find any.

I wasn't the one who suggested that the Greenman might have been a Firstborn. While applying the term to him would explain his unusual identifier, should he happen to be a Flower, I'm fully aware that the Firstborn concept was your creation, enacted years after the departure of Jay and Acacia to explain why some Flowers have names while others do not. It wouldn't have been mentioned within the Original Series itself.

Actually, now that I think about it, the Greenman might not be part of Upstairs at all. The plants Upstairs were usually obeyed and minded by the Agents, albeit in a chiefly mocking and sardonic manner, while the Greenman's only appearance seems to characterize him as a put-upon instructor who was never taken seriously by his students and mostly wanted them out of his sight as soon as possible, which doesn't fit with the rest of the PPC officials we see in Jay and Acacia's missions. He could easily just be some guy assigned by what we would now call the Department of Operations to supervise processes like an Agent's first lightsaber training because, as you said, someone's got to do it. He could easily just be some plant-based alien who was named Greenman upon recruitment or mockingly given that name by his students.