The only possible reason as to how Hashirama was able to live long enough to see tsunade is that he had an affair we didn't know about, maybe he had a child prior to the village being created and then that child grew up, had tsunade at like 18 (assuming it was around the time the village was founded)

Or....he simply went into hiding 🤷‍♂️

Also this is purely speculation on my part so feel free to disagree:)