Check the distance between the 2 metal rails of the mount you're buying, if the hole is large enough for the vesa mount to hang on the rails, fasten the rails across the hole to the sides of the shelf with the angle bars running continously from top to bottom at the sides in a single piece and hang the TV on the rails. To avoid the mount from breaking through the wood and falling out forwards, attach addition metal rails perpendicular to the angle bars so you can additionally screw it further in the shelf as reinforcement