Take the drawer and drill a slight hole on the 4 corners of the front inside of the drawer leave at least 5 1 space from the ends this is where the screws will be placed to add the front.
Attaching shaker drawer fronts.
Make sure the slight hole is only deep enough for the screws head.
I make videos 3 times a week on diy home projects and just lifestyle videos.
You could also run your drawer handle through the panel and use those screws to help hold the front on with some screws on the side into the stiles.
Then you d have more thickness to screw into.
It will be level with the drawer after installed.
I think a better alternative if you re set on this design is to use a 1 2 panel.
Hope this helps some.