Wellll you could technically jam their uplink channels, but doing so may get the US in your doorstep quite quickly
I don’t think the almanacs are necessary for the system to work, in theory. But I believe they’re commonly used by receivers to narrow down the range of possibilities when trying to find a PRN match for a signal they’re getting.
(I’ve dealt with GPS and similar navigation signals for work but am not an expert, this is just the impression I’ve gotten over a few years)