Making a Hall effect sensor into a PCB
I did this very experiment in physics class, upper school. We used the thinnest aluminium foil available, with a very significant current, in the 1A ballpark, and a very strong magnet. The actual voltage generated was very small, barely detectable.

Commercial Hall elements use semiconductors, which have carrier densities orders of magnitude lower than that of metals, so have a Hall coefficient orders of magnitude greater.

To deal with the poor sensitivity, you would have to use a high current, a thin foil, and either a chopper/zero drift amplifier for DC excitation, or AC excitation and synchronous demodulation. It's not impossible, just very hard, and probably more expensive (to get the same sensitivity) than buying a commercial Hall IC and mounting that on the board.