I recently finished my first kit build. It was a tele kit from Thomann (Harley Benton).
I replaced the bridge with a 6 saddle bridge, and that one was a bit thicker, so the action got higher.
Even when the saddle is as low as can get it it is about 2mm on the high E (bottom to 12th fret).
I tried to raise the neck a little bit by putting some paper (about 1mm thick) under the neck, to try to lower the action by raising the neck.
It didn't seem to have much effect.
I was considering two options:
1. putting more paper or something else (veneer?).
2. drilling the screw holes in the body a little bit wider so that the screws become loose in the body (now there is internal thread in the body and the neck). then there will be a gap between the neck and the body. The screw heads and metal plate will attach the neck on the body, and the internal threads in the neck.
Then the four screws could be used to raise or lower the neck as well as adjusting tilt.
other options could be to get a thinner bridge or remove wood beneath the bridge. Those sound less appealing to me.