Yes — this is normal if the camera is not cocked. On the AE-1 Program, the aperture stop-down/DOF preview mechanism needs the camera to be cocked via the film advance lever. If you test depth-of-field preview without cocking it first, the lens may not stop down correctly and can appear stuck around a wider aperture such as f/4.

Since it worked normally once the advance lever was cocked, that indicates the camera is likely fine and this should not limit your aperture during actual shooting, as the camera is cocked when ready to make an exposure. In short: it was a testing/setup issue, not necessarily a fault with the body or lenses.