Yes, it might be possible to fix.
Yes, it might be possible to fix.
Could you provide a clear image of the socket? This helps confirm whether the pin is crucial or just for power. If it's only for VCC or VSS, you might lose a few connections and still function. But if it's a data pin, flip the board upside down and shake it to remove the pin safely. For a permanently affected data pin, you'll need to replace the socket using BGA rework tools—expensive if you do it yourself. Even for a one-time project under $100, building the board is unnecessary if it's just a temporary fix.
I wouldn't manage that board with a 11900k anyway. Who instructed you to match those?