First we'd have to establish why it didn't close off (or why it stopped being closed off). And theres several options for that
1. Another Family wins the powergrab at the end of Sengoku Period, or Oda Nobunaga (initial winner) stops the last revolt by the Toyotomi and Tokugawa clans ... Easiest would be to butterfly away Akechi Mitsuhide's coup d'etat, who made an internal powergrab forcing Nobunaga to commit suicide, so that the Oda's keep the power. and since Nobunaga was a Military genius and was as active as you could on the international scene he should be able to keep the seat as the most important man in Japan (traded with the Portugese learning how to make muskets for one). add to that that he developed the Japanese industry and farming nearly just as much as it was doing the Meiji period (at least relatively), and started trade routes with Korea, China, Europe and Southeasten Asia such as Philippines, Siam and Indonesia (and would likely keep expanding those Trading routes)
Given this expansive and trading oriented leadership, and lacking the Tokugawa's Arcane rules (of which a popular history is that he banned the wheel, since it would make transportation to easy ... someone once said that it cost just as much transporting goods 50 miles inland in Japan as it cost to transport the same goods from Europe to Japan) Japan would likely consolidate and be a viable contestent for the regional power allready from the early 1600's, prehaps even capturing whatever weak land there were around, or expanding the traderoutes around India and trading with the Arabs.
2. one of the Tokugawa heirs was a progressive rolling back many of the arcane rules and started to promote trading other than with the Dutch via a small islet in the Nagasaki habour
3. Much earlier revolt of the revolt that would end out in the Meiji Period, which would have to evolve from earlier pressure from the european/American naval powers (America, Russia and prehaps even Netherlands and whoever hanged around in the west pacific at that time) forcing the Shogun to open op trade more, and young dissatisfied samurais importing (illegal!!) superior firearms from 'outside'
Easiest would probably be to butterfly away Oda's death and take it from there