....We know that the antichrist has to subdue a few kings which right there tells us that the whole world just doesn't bow down to this new guy on a white horse right away. He has to subdue them... that's the 2nd horse, and the third and fourth horse are the things that have followed war across the ages.
By the midpoint of Tribulation, the antichrist will have most of the world subdued and will make demands of everyone on the globe. Get the Mark, worship the Beast., etc. By then the world will be a horrible mess and the world population will be greatly diminished.
That is my understanding as well.
He enters the stage in the first seal. This is after the Rapture- because from the end of Rev 3 onwards, the church is seen in heaven, including the interval before the Seals begin to be opened by Jesus.
Confirmed by Paul in 2 Thess 2:1-8 when Paul outlines the order of events surrounding the Rapture. The AC cannot be revealed, while the church is still here, because the Restrainer is still restraining until He be taken out of the way (referring to the Holy Spirit working thru the church here on earth) and the subject is the Rapture.