Gutenberg does seem to have been the first to devise a printing press, but printing itself, that is, making multiple copies of a text by transferring it from one raised surface to other portable surfaces (especially paper) is much older. The Chinese were doing it as early as the 4th century, and the oldest dated printed text known to us is from 868: the Diamond Sutra, a Chinese translation of a Buddhist text now preserved in the British Library.
What is much less well known is that, little more than 100 years later, Arab Muslims were also printing texts, including passages from the Qur'an. They had already embraced the Chinese craft of paper making, developed it and adopted it widely in the Muslim lands . This led to a major growth in the production of manuscript texts. But there was one kind of text which lent itself particularly to mass distribution: this was the private devotional collection of prayers, incantations, Qur'anic extracts and the "beautiful names" of God, for which there was a huge demand among Muslims, rich and poor, educated and uneducated. They were used especially as amulets, to be worn on the person, often rolled up and enclosed in a locket.
So in Fatimid Egypt, the technique was adopted of printing these texts on paper strips, and supplying them in multiple copies to meet the mass demand. Several have been found by archaeologists in the course of excavations at Fustat (old Cairo), and the archaeological context has made it possible to date them to the 10th century.
So Muslim printing continued for about 500 years. We do not know whether it may have influenced the eventual adoption of printing in Europe: there is no evidence, but the possibility cannot be ruled out, especially as the earliest European examples were block-prints.
What is not in doubt is that Muslims were practising the craft of printing for some five centuries before Gutenberg.
Muslim Printing Before Gutenberg, By Geoffrey Roper