Jewish written history witnesses that The Cross immediately changes their relationship with God

Based on the Talmudic accounts found primarily in Tractate Yoma 39b, the final forty years of the Second Temple (c. 30–70 AD) are depicted as a period of escalating spiritual decay marked by four specific, recurring failures in the Temple service.

For the four decades from the crucifixion to the destruction of the temple, it operated under a cloud of divine disfavor.

Every year on Yom Kippur, the High Priest would cast lots to determine which goat would be sacrificed to the Lord and which would be sent away as the scapegoat. Historically, drawing the lot "for the Lord" in the right hand was seen as a sign of God's acceptance. However, for forty consecutive years from the crucifixion to the destruction of the Temple, the lot consistently appeared in the left hand, a bad omen that unsettled the priesthood. They recorded this.

Simultaneously, the ritual of the scarlet thread ceased to function. According to tradition, a crimson strap tied to the Temple door (and another on the scapegoat) would miraculously turn white upon the acceptance of the sacrifice, fulfilling the prophecy that sins would be made "white as snow." From the crucifixion onward, the thread remained stubbornly crimson year after year, signaling that the atonement was no longer being accepted.

Inside the sanctuary, the western lamp of the golden Menorah, which was supposed to burn perpetually, began to flicker and go out daily despite the priests' best efforts to keep it fueled. This extinguishing of the light was viewed as the withdrawal of the Divine Presence from the Holy Place.

Most terrifying of all were the massive Temple doors. These heavy gates, which required several men to operate, began to swing open by themselves every night. The phenomenon continued unchecked until Rabban Yohanan ben Zakkai, a leading sage of the time, rebuked the sanctuary. He cried out, "O Temple, why do you frighten us? We know you are destined for destruction," citing the prophecy of Zechariah regarding Lebanon's doors being opened to fire. These events served as a somber, forty-year countdown to the Temple's ultimate destruction in 70 AD.

The Jews don't write 'oh crap we killed the Messiah' but they do very clearly record how their relationship with God shifted.