well, nimaiyo is the creator of the zanpakuto. since he himself is a shinigami, it only makes sense that he would have had the first zanpakuto. also, they call yama's blade ancient, never the first. actually we haven't seen many fire type zanpakuto at all.This chapter tell me the opposite.
Yamamoto was said to have oldest zanpakuto overall, or oldest fire type zanpakuto. If he has oldest zanpakuto overall than it's pretty clear who is older. If he only has fire type zanpakuto than it's pretty much the same since fire type zanpakutos are mostly used zanpakutos. In both, Yamamoto is one of the first shinigamis that get their zanpakutos.
Ichibei implied in this chapter that before him bankai was called different, which mean that there were a lot of bankais before he learned his.
ichibei doesn't even call bankai, bankai. which gives the impression that he is used to calling it "true strike" or whatever the chapter called it, or simply referring to it as the evolved form of the zanpakuto. he made a point to say kids now a days call it bankai. meaning that he later decided to name it this. nothing in what was said gives the impression that there were many bankai before he learned his. just that he didn't name it until much later.