If there was any necessity for people back then, or today, to know "the exact moment" when those things were hidden from the Jewish people, the scriptures would have stated it. As it was, Jesus indicated that it was "this day" - the day he was speaking. We do not know the hour, and we cannot date the day exactly.
Yet those listening to him would know. And those disciples who had asked Jesus questions and received his reply would know that the day of grace for the nation of Israel had ended, that day. From there-on-in, those who had failed to see Jesus as the promised Prince of Peace would be unable to see with their spiritual eyes the things that would have made for peace. Their "day of visitation" had come with the arrival of the messenger hearlding the Messiah who was now soon to be crucified, at the clamour of the Jewish crowds, who would carelessly request that the blood of Christ be upon them and their children (Matthew 27:25). Certainly by then, that appalling statement proved that Jesus' prophetic words about things "hidden from their eyes" had already come to pass.
Nor was it just the Jewish people who had such things hidden from their eyes back then. The apostle Paul wrote,
"We speak of God's secret wisdom, a wisdom that has been hidden and
that God destined for our glory before time began. None of the
rulers of this age understood it, for if they had, they would not have
crucified the Lord of glory" (1 Corinthians 2:7-8 - emphasis mine).
They did not understand they had been in a period of 'visitation'. Yet, at the birth of John the Baptist (a few months before Jesus was born), his father Zacharias miraculously spoke and
"...was filled with the Holy Ghost, and prophesied saying, 'Blessed be
the Lord God of Israel; for he hath visited and redeemed his people...
And thou, child, shalt be called the prophet of the Highest: for thou
shalt go before the face of the Lord to prepare his ways... whereby
the dayspring from on high hath visited us, to give light to them that
sit in darkness and in the shadow of death, to guide our feet into the
way of peace" (Luke 1:67-79 - emphasis mine).
Those Jewish people who heeded John's preparatory ministry to repent and be baptised, were prepared to then receive Jesus as the Messiah, 'the dayspring from on high'. Their feet were guided into the way of peace, to sit at Jesus' feet, the Prince of Peace. Alas, all those who dismissed John's gospel message also dismissed Jesus' preaching and call to repentance. That brought on spiritual blindness, and heading into disaster, when they could have walked in the light and peace of Christ.
By the time Jesus wept over such ones in Luke 19:42, that day of visitation turned into a day of judgment for them, but that spiritual blindness began to set in with rejection of John the Baptist's preparatory work.