With TWO coats of adhesive on both surfaces the first panel can be laid on to the box. Start at the center line and carefully line up one edge of the panel as shown. Like this the glue will not grab a hold and you can manoeuvre the veneer piece into the correct position. Once the piece is lined up run a finger along thefirst edge to make the glue grip and then progessively work the rest into position rubbing along the grain.
Do not just drop the piece down flat and then apply pressure as this will encourage the formation of air pockets
The idea is to roll the piece of veneer into contact and then apply pressure as you go.