Double check that the output jack connections are correct. It’s easy to get the ground and hot connections swapped over and if you do that, the pickups still work but any shielding is now carrying the hot signal and acts like an aerial and picks up hum.

Also that for the volume pots that the tab the other end to the input connection is connected to ground. Some of the kit diagrams show it bent back to touch the casing but not actually soldered (which it should be).

Have you got a multimeter? If you have, then check the continuity of the ground connections for low resistance. The ground resistance path should be as close to zero as possible, and only just over the ohms value you get when holding the two probe ends together. If you haven’t, then you really need one. Even cheap ones work well.