When was Japan named after the meaning "land of the rising sun"?

Question

Was it long before the advent of writing?

Answer 1

The kanji characters that make up "Japan" literally mean "sun-origin". That is where the phrase "land of the rising sun" in reference to Japan originates.

After doing a quick little search...
WORD HISTORY Stamp collectors know that Nihon and Nippon on Japanese stamps mean “Japan”; what they probably don't know is that Nihon, Nippon, and Japan are all ultimately the same word. In the early part of the Chinese Tang dynasty—in A.D. 670, to be precise—Japanese scholars who had studied Chinese created a new name for their country using the Chinese phrase for “origin of the sun, sunrise,” because Japan is located east of China. In the Chinese of the time (called Middle Chinese), the phrase was nzyet-pwun. To this the scholars added the Chinese suffix –kwuk, “country,” yielding a compound nzyet-pwun-kwuk, “sun-origin-country, land of the rising sun.” The consonant clusters in the word were not pronounceable in Old Japanese, so the form was simplified to Nip-pon-gu or *Ni-pon-gu, the latter developing by regular sound change to Ni-hon-gu. The forms Nippon and Nihon of today are the same as these, minus the “country” suffix. Interestingly, the Chinese themselves took to calling Japan by the name that the Japanese had invented, and it is from the Chinese version of the name that English Japan is ultimately derived. In Mandarin Chinese, one of the forms of Chinese to develop from Middle Chinese, the phrase evolved to Rìběnguó, an early form of which was recorded by Marco Polo as Chipangu, which he would have pronounced as (chĭ-pän-gū) or (shĭ-pän-gū). The early Mandarin word was borrowed into Malay as Japang, which was encountered by Portuguese traders in Moluccas in the 16th century. These traders may have been the ones to bring the word to Europe; it is first recorded in English in 1577, spelled Giapan.

Answer 2

The kanji characters that make up Japan's name mean "sun-origin", which is why Japan is sometimes identified as the "Land of the Rising Sun". Therefore it was after the development of Kanji script in the 5th and 6th century.