The easiest way to maintain water resistance is to not puncture the enclosure.
It looks like the box has holes extending through the cover down to the bottom, I'm guessing these are specifically for mounting? (The 2 large holes). Use those if you can.
The next best option would be to attach the box so that the bottom is against the plate, and screws come in from the outside into the screw holes that extend from the top of the box to the bottom.
Another option is to attach the plate with screws from the inside. Place the holes so the inner surface around the hole is flat, and then use sealing screws.
Depending on how water proof you need the box to be, it might also be viable to just mount the box using angle brackets so the screw holes are facing the ground. Although not fully waterproof, water would be unlikely to get in that way.