A thrust chamber is not “boundless”; it has a finite volume, a fixed inlet area, and a fixed outlet area. When fuel and oxygen are injected into the chamber, the flow rate in is greater than the flow rate out, as you have agreed that the flow rate out of a chamber is limited.
So, just as the water level in a leaky bucket can rise if the flow rate in is greater than the flow rate out, the pressure in the chamber rises. Then, when ignition occurs, it occurs not in zero pressure.
Correct. But once iginition happens, you no longer have a vacuum in a chamber that resembles the “endless, boundless absolute vacuum of space”, so the leaky bucket analogy doesn’t hold.