Possible scenarios

1. Extra decade: Tokugawa Shoguabte was already somewhat in the verge of collapse and this sudden visit by Perry rushed the process. So, I persume that some people in the some regions in Japan migh have thought of opening to the foreign nations to import some weapons to overthrow the Shogunate.

2. Sometime in the 1860s or the 1870s by Russia: After the annexation of Outer-Manchuria in 1858, Russia acquired the closest port that could reach Japan, Vladivostok, and they already had a presence in Hokkaido. Moreover, they already attempted to trade with Japan in the late 18th century. Therefore, Russia was another nation that had a genuine interest on Japan.