What if "the part where the PCs have agency" is while they are still tied up? Sometimes "exercising agency" involves recognizing the wall and admitting that you've got nothing and as a group are choosing to wait for some future point in time when there is a change to the scenario where they know X Y & Z but don't feel like they can see a way over/around Z because of an assumed P & Q.That's fine, but I still say skip (by way of narration) to the part where the PCs have agency.
"Six weeks ago, you woke in Lord Terrible's dungeons, and despite all your efforts you have not been able to escape. For the first time since your imprisonment, Lord Terrible has come to oversee your torture himself." And then play, or whatever. There is no need to play out those 6 weeks. If the PCs have no agency, they aren't relevant to play.
Maybe that admission leads to understanding that P & Q are not as solid as assumed. Maybe it leads to a future point in time where X Y or Z is changed in some way & the PCs now have new options. Through an admission like that the GM knows why the players "feel" they lack the ability to exercise their agency and reveals any faulty assumptions held by either side of the GM-screen so they can be clarified.