So I had this idea for an FTL drive that would work by creating a rift (a black hole before it tugs on space enough to become unstable and deadly) via an unbelievably strong magnetic field. I know that atoms are mostly empty space anyway, and they can be compressed to smaller sizes with a big enough applied force. But could a magnetic field actually produce a force capable of squishing a matter (probably plasma) down to the point where it would become a black hole?
Yes. See for example The Z Machine for ideas.
You can also find videos where a metal object like a coin in crushed using such effects.
Look at the fields involved in Magnetars, and that’s not enough to crush matter beyond nuclear densities. But using pulsed power, small regions, and invoking quantum gravity effects you can get away with it. Quantum gravity is a big unknown right now, and that gives you room to paint whatever you like without violating the known laws of physics.