Hi Maxence,
The bridge is a floating design. It does not need to sit on the body.
On the JM-1L I built, the bridge is 4 to 5 mm above the body.You can see the gap in the photo.
Attach the neck with the screws and then wind the posts out until you get no fret buzz.
This link is a better photo of the bridge. http://www.buildyourownguitar.com.au...2&d=1508666479