The messiah's ministry is not mentioned in the text of Daniel 9. The thinking that Jesus was cutoff in the middle of the seven years is not in Daniel 9:27. That particular thinking is a construed interpretation that some make. John 12:1-15 provides the correct interpretation of the messiah's arrival and being cutoff.
I presented John 12:1-15, as the messiah's arrival in Jerusalem, the passover week he would be cutoff, crucified. Fulfilling Daniel 9:25-26, regarding the messiah's arrival in Jerusalem and his being cutoff.
The 70th week is treated separately from the other 69 weeks (483 years). Daniel 9?27 begins with the confirming of the covenant for 7 years and then in the middle part of the 7 years the daily sacrificed stopped and admonitions begun.
If we were living at the time of Jesus, first century, having this discussion - then no, we could not have foreseen that the 70th week would be over 2000 years later. But now, in hindsight, we know there has been a gap of 2000 years.