Mid 1500s is the height of the Warring States period in Japan (1477-1603). If by common Japanese you mean ordinary peasants and townsfolk, then I am going to guess no in the mid 1500s. They had more important things to worry about (ie survival). Among the aristocrats, samurai, and the rich, books (particularly religious texts) were available by the 1200s.

In the Edo period (1603-1868), the Tokugawa shogunate created a stable and peaceful society. And with European, Chinese, and Korean know-how of publishing now in Japan, books began to be printed.

So in the Genroku period (ca1675-1725), ordinary townsfolk became wealthy enough to own books. And even if they could not own books, they could rent books. Ihara Saikaku (1642-1693) wrote books about commoner life: Life of an Amorous Man, Life of an Amorous Woman, Five Women who Loved Love, The Great Mirror of Male Love. The poet Matsuo Basho (1644-1694) published his compilation of poems Oku no hosomichi (Narrow Road of Mutsu province) and described the scenery of northern Japan.

By the Kasei period (ca1800-1830) education spread to peasants so that more commoners could enjoy books. Japan had one of the highest literacy rates in the world in the 19th century at around 60% in cities and 20% in the rural countryside, something like 50% for the entire population. [Only Europe and North America comes close or surpasses these numbers. Literacy in China was under 20% in the 19th century.] This is when authors like Kyokutei Bakin (1767-1848) wrote adventure novels like Nanso Satomi Hakkenden (Tale of 8 Dogs) and Jippensha Ikku (1765-1831) wrote comedies like Tokaidochu Hizakurige (The Shank's Mare).

Because there were no libraries in the Edo period (gotta thank Benjamin Franklin for spreading them in the US), book lending remained a major business in Japan even after the Edo period: Kashi-hon business. Not enough libraries were built in pre-WW2 Japan. Today Japan has a big publishing industry and an elaborate library system.

So 3 line summary. (a) books for only aristocrats, samurai, and rich in the mid 1500s. (b) townsfolk start reading books in late 1600s. (c) everyone starts reading books in early 1800.