It would have been the Meiji Era, which started in 1868, though giving it some time is likely, translated novels would have probably been widely available in the 1880s at the latest.

Before then, the most common translation of Western literature would have been Christian bibles, ostensibly because of the missionary efforts of various Westerners.

There's also the problem of what 'normal' Japanese people would be buying as many people may not have been literate enough to partake in reading novels throughout various periods of Japan's history.

Also, the import of books would have been low before this period as trade with Westerners itself was heavily restricted until the opening of Japan after Perry's famous visit.

But once the Meiji Era began, literature of all sorts poured into Japan while literacy rates shot up with school reforms.

What is interesting is that many of the translations of literature wouldn't have been from English (or French, German, Russian,etc) into Japanese. Rather, especially in the beginning, most of the translations were made from Chinese translations of famous works.

This is due to the lack of qualified and experienced translators who had the knowledge and skill to translate from Western languages to Japanese, which itself was due to the fact that Japan had only limited contact with the West before the Meiji Era. Meanwhile, the Japanese and Chinese languages are much more similar, relatively speaking, which greatly facilitated early and quick dissemination of a lot of key works of Western literature.

China's intellectuals had long been exposed to much of the West's great works in medicine, philosophy, novels and essays. Balzac, Hugo, Shakespeare...

Much of Japan's first translations came via Chinese to Japanese translation. Meanwhile, Japan sent a veritable army of intellectuals to Europe to study among them, learn their language and ways, and bring back anything and everything that would be useful, novel and extraordinary to those back home.

As for the physical books themselves, Japan (and China and Korea) had been printing books for a long time. The game changing Gutenburg press had already been in Japan nearly 300 years before, since the early 16th century, so they had no problems printing books for people who wanted them.

European styled bookstores would have come later, though books could be bought in regular markets, from traders, institutions of learning or archival, etc.

All this being said, Japan's government's focus was mainly on works about politics, governance, military and medicine, scientific knowledge. Literature would have had its place but the government's focus would have been elsewhere, meaning better translations of literature and play would have been longer in coming.