An open bite is usually when the upper and lower teeth do not meet/overlap at the front. Thumb sucking is a common cause. The upper teeth edges can be 5-10 mm away from the lower teeth edges and placing veneers on the upper teeth will produce very very long teeth. The correct treatment is orthodontics whether it be fixed braces or Invisalign.
Most esthetic, most conservative and least expensive way to correct this is with orthodontics, traditional or Invisalign. It will take more time but it is worth it.