Are we living in the Last Days? Yes! and we have been since the days of Acts Chapter 2:
Acts 2:16-17 But this is what was spoken by the prophet Joel: ' And it shall come to pass in the last days, says God, That I will pour out of My Spirit on all flesh; Your sons and your daughters shall prophesy, Your young men shall see visions, Your old men shall dream dreams.
Peter declares that the Last Days began some 50 days after the Resurrection of Jesus because of the outpouring of the Holy Spirit.
We also see this in Hebrews:
Hebrews 1:1-2 God, who at various times and in various ways spoke in time past to the fathers by the prophets, has in these last days spoken to us by His Son, whom He has appointed heir of all things, through whom also He made the worlds;