I'd assume Roman probably. We know that there are submerged pots meaning they're made of a material that doesn't erode in water over extended periods of time. A good examples of a material like that would be stone but since those are difficult to shape, it's unlikely that any ancient civilization used them to create pots, at least in the sense the player character would be able to recognize. Most likely, the pots are made from baked clay, a process which was popularized in Europe by the Greeks and adopted by the Romans. Metal is another viable option, though if it was something like a bronze or iron age pot, it would make sense for the character to grab those as well since the decay would be minimal on those compared to clay pots. They would be significantly more recognizable compared to submerged clay pots making them more valuable when selling. I'm no historian or archaeologist but this is what I've surmised from the barebones information we've been given in the game. Definitely open to any other ideas about this in terms of what people have to say.
TL;DR: probably Roman, seriously though, who knows?