The issue of when the scrolls were composed or copied has much to do with when the Essenes or "Dead Sea Scroll People" emerged in history. The prevailing opinion is that they emerged in the early second century BCE either as a response to the oppression of the Seleucid period or the continued Hellenization under the Hasmonians when the High Priesthood was usurped by a non-Zadokite. Although some of the biblical texts could predate this period, it would place the composition of the earliest sectarian texts between 175-150 BCE. An hypothesis that intrigues me has been offered by Fr. Jerome Murphy-O'Connor of the Ecole Biblique in Jerusalem. Relying strongly on clues in the text known as the Damascus Document, Fr. Murphy-O'Connor suggests that the Essenes had their origins in Babylonia during the Judean exile following the destruction of the first temple in 586 BCE. Some of the group may have returned to Judea during or shortly before the Maccabaean revolt. Clues for this hypothesis can be found in the Damascus Document, CDa, CDb (Cairo Genizah), 4Q266-272 (DSS). CD presents an historical account that ends with the exile. it gives an account of leaving the land of Judah and going to the land of the north. Since much of the legislation in CD governs a Jewish community among non-Jews, CD may hail back to more ancient times to the community living outside of Palestine and the Essenes may have existed long before the Teacher of Righteousness.
My late mentor, Dr. Bill Albright, one of the foremost palaeographers and orthographists of our time, believed the Great Isaiah Scroll (1QISa) had definite indicators of Babylonian origin. It may be reasonable to assume that some of the older texts of the DSS were brought to Palestine from Babylonia by these returnees. The range for the copying or composition of the DSS could span the late 3rd century BCE to the end of the 2nd temple period in 68 CE.
Scholars continue to debate when the scrolls were cached in the eleven (or more) caves along the western shore of the Dead Sea. In the center of this debate is the word KITTIM mentioned frquently throughout the texts. KITTIM means "people of Cyprus" and certainly originally referred to the Seleucids. It appears, however, to have become codified for any invader of oppresser from the sea to the west and was later applied to the Romans. The "Slain Messiah" text (4Q285) has been interpreted to refer to the Romans as illustrated in my reproduction of the fragment below:
The word "kittim" appears partially in the lacuna at the very bottom of the fragment.
Line 1 ..Isaiah the Prophet .
Line 2 ..The septer shall go forth from the root of Jesse ..
Line 3 ..branch of David and they shall be judges ..
Line 4 ..and they put to death the leader of the community, the branch
Line 5 ..with piercings and the priest shall command .
Line 6 ..the slain of the Romans .
Were the scrolls cached during the "kittim" oppression of the Seleucids, the "kittim" conquest under Pompey, or the "kittim" conquest of the 1st Jewish War? The debate continues.