I think its fair to say that everyone here has strong opinions on the towers, but also that much of the lore surrounding them is misleading. Primarily, I'm thinking of the accepted gospel that Adamantia is the original tower and that all the others are echoes/reflections of its design and intent.

This is explicitly stated for White-Gold and the Crystal Tower, but not so much for the others. We don't know enough about the Orichalc Tower to say much either way, but it seems plausible to assume that either the Sinistral Mer or the Yokudan men followed a similar process of replicating Adamantia. The same can be said for the Coral Tower, regardless of whether it actually functioned as intended. Everything about the Numidium is weird, but again, it at least seems to replicate the same concepts.

The creation of Adamantia is taken as the beginning of linear time, meaning it is inherently the oldest thing on Nirn, but we know that there were non-linear, initially ageless beings and objects in the Dawn Era. Anything that existed before/simultaneously with Convention are necessarily just as old/older than Adamantia.

At a very basic level, Red Mountain's origin story contradicts the generalization of the towers. It rose independently from the Heart of Lorkhan simultaneously with Convention. It was not created by Mer in imitation of Adamantia. It wasn't really "created" at all. It seemingly stands apart from the accepted wisdom about the other towers' relation to Adamantia. If you accept that the towers stand at the joints of the Earthbones as described by Subtropical Cyrodiil: A Speculation , then it seems as if god/bone most directly connected Red Mountain is Lorkhan himself, who is fundamentally not an Earth Bone in the same way as the other gods. Of course, the text is also literally "A Speculation," which immediately casts doubt on its conclusions from a meta perspective.

Then there's Greensap, another tower created by Mer, except its the tower associated with the least Aldmeric of all the Mer. Both the Bosmer and Khajiit creation myths challenge the assumption that they followed the same breakaway process as the other Elven races, and the Bosmer tradition explicitly connects their origins to the Ooze. It suggests a creation in a still unstructured period like the Dawn Era. We don't know exactly when Greensap came into being, but with Y'ffre as the supposed "First Earth Bone" and The Ooze: A Fable claiming that Y'ffre created the Graht Oaks before even the Bosmer themselves, there's room to view Greensap itself as a pre-convention tower.

Finally, we turn to Snow Throat. Technically speaking, nothing confirms that it's the Throat of the World, but it is strongly suggested. Red Mountain at least speaks to the possibility. Like Red Mountain and Greensap, the mythology of the mountain doesn't really line up with the explanation that it was constructed or turned into a tower by Mer. True, we don't know enough about the Snow Elves to really know how they related to the giant mountain in the middle of their territory, but Nordic mythology suggests that humans were created there by Kyne, an event seemingly from the Dawn Era. Paarthurnax and the Greybeards certainly keep the place tied to Kyne in some way. I think this also points to Snow Throat as a pre-convention tower in the same vein as Red Mountain and (potentially Greensap).

There is definitely a counter to that interpretation though. The usual wrench in interpreting the Throat of the World as Snow Throat is MK's declaration that the stone is "the cave." That interview happened in 2013, after Skyrim and all its DLC's came out. So I think it's fair to say that even once the game was complete, MK at least thought his interpretation of "the cave" was correct. You can take that in all sorts of metaphoric directions. I'm personally fond of the idea that the extremely strict interpretation of the Way of the Voice practiced by the 4E Greybeards can be compared to Plato's Cave. However, I think there's also a good, literal view of the cave stone in Skyrim as well: Eldergleam Sanctuary. Like the mountain, the Eldergleam is sacred to Kyne. It's in a cave. We even leave it "sundered and bleeding" depending on which choice the player makes.

Eldergleam was supposedly planted in the Merethic Era, which would potentially rule out Snow Throat as pre-convention. Greensap still leaves me wondering though.