From my research into the precursor of Go, the honest answer I can say is I don’t know. However we also need to realize that like the evolution in biology, the evaluation of Go weren’t linear. It’s not a simple one game progressively evolved into the next version, but branching into many variations and some of them survived for various reasons.
From the documents survived today, I am pretty certain that 17x17 and 19x19 boards co-existed between the Han Dynasty and before the Tang Dynasty. And not just board-size, but other rules from ko, to fixed placement stones, to even possibility the scoring methods were also varied. Even smaller board size like 13x13 15x15 existed during or even after this time period, and there were evidence that not just Go were played on them. It is fairly easy for different rules and boards to diverse and be kept in ancient time when communications are difficult (especially during divides when wars separate different regions)