This is a twofold question, it would be best if I answered the second before the first. It should be noted that the origin of Beowulf, specifically as an Old English poem is up to debate. Scholars have argued for a quite a long time concerning where it falls on a massive scale of time, 700-1000 A.D. The oldest date that it could possibly be from, according to such estimation, is the 8th century. However, the earliest manuscript that we have for Beowulf, Cotton Vitellius A.xv, has been dated from between 975 and 1025.
Onto your first question, writing emerged in Scandinavia in the form of runes (Elder Futhark) around the year 100 A.D. However, it would perhaps be even earlier, if we account for the time that it took for the art form to spread. Whether you'd consider this literature is a bit iffy. Literature implies a full-length written work, whereas runic inscriptions typically kept to short passages. If we discount runes and only consider full-length material written in manuscripts with the Latin alphabet, then Beowulf likely was written earlier, since most of Scandinavian literature was composed between the 12th and 13th centuries.
Still, this is limiting stories and knowledge to a specific form, in this case, written form. Beowulf and many other stories were told and received orally long before they were written down. Stories can certainly exist without being written, although this creates some interesting effects. I won't turn this answer into an article on the foundations of literature, but you get the idea. I'll add that there are runestones containing excerpts of similar stories, such as the Völsunga saga that date to around the same time as the manuscript containing Beowulf.
There is a series of runestones known as the Sigurd Stones, broadly dated to 950-1000 A.D., which would make them roughly contemporary with Beowulf if you go by the Cotton Vitellius manuscript. These were written in runes (Younger Futhark) and contain portions of Sigurd’s story. While it could not be considered a full-length work like Beowulf, Scandinavians were still writing bits of their own stories down around the same time. the events in Völsunga saga took place in the fourth and fifth centuries, which is earlier than the events of Beowulf, which took place in the sixth century.
Michael P. Barnes, Runes: A Handbook (Woodbridge, UK: The Boydell Press, 2012), 2-3.
Jesse L. Byock, “Introduction,” in The Saga of the Volsungs, translated by Jesse L. Byock (London: Penguin Books, 1999), 2.
Michael Alexander, “Introduction,” in Beowulf: Verse Translation, translated by Michael Alexander (London: Penguin Books, 2003), 1.