As usual, the scholarship of the WT writers is questionable to say the least. To make matters worse, they do not quote sources. The reader is forced to take their word for it. Perhaps they should try doing it this way, so that those who are interested in the subject can do their homework and decide for themselves:
The Jews did expect “Messiah [the] leader” at the beginning of the CE (Matt. 2:3-6). This has to do with Jewish reckoning, especially Essene chronology. According to R. Beckwith: “The Essenes began Daniel’s seventy weeks at the return from the Exile, which they dated in Anno Mundi 3430, and that they therefore expected the period of seventy weeks or 490 years to expire in A.M. 3920, which meant for them between 3 B.C. and A.D. 2. Consequently their hopes of the coming of the Messiah of Israel (the Son of David) were concentrated on the preceding 7 years, the last week, after the 69 weeks. Their interpretation of the seventy weeks is first found in the Testament of Levi and the Pseudo-Ezekiel Document (4 Q 384-390), which probably means that it was worked out before 146 B.C.” For a more complete discussion of the evidence see Roger Beckwith, “Daniel 9 and the Date of Messiah’s Coming in Essene, Hellenistic, Pharisaic, Zealot and Early Christian Computation,” Revue de Qumran 10 (December 1981): pp. 521-542.