If the Rapture is right before the arrival of the Antichrist, and 10 kingdoms come first (Daniel 7), how can it be imminent?
You are correct that Daniel says there must be 10 kingdoms over the world before the start of the Tribulation and the rise of the antichrist, but the Bible also teaches that the resurrection (i.e., rapture) is imminent for every generation of Christians and that the resurrection must take place prior to the revealing of the antichrist.
How do we reconcile these details? The answer is the Bible never makes a connection between the timing of the resurrection and the start of Tribulation except that the resurrection must occur first. In other words, the Bible never specifies how much time must pass between the resurrection of the church and the start of the Tribulation. It could be a short time, but it could also be a very long time. We don’t know.
The Bible makes no claims for how long the world will wait after the resurrection of the Church before the appearing of the antichrist and the start of Tribulation. While most Bible scholars assume there will only be a short gap of time between the resurrection and the start of Tribulation, it is possible for the two events to be spaced many years apart. The only thing we know is the resurrection is imminent and must come first.
The rise of a ten-ruler government could also happen at any time. It is not dependent on the resurrection either. These rulers could rise to power before the resurrection of the Church or after the resurrection. So, the resurrection could happen at any time, and the rise of the ten rulers could happen at any time. Following the arrival of the ten rulers and the resurrection of the church, then the antichrist will be revealed and the Tribulation may begin.
If you want to hear the full details of this sequence, we highly encourage you to listen to our Revelation Bible study, available for free here.