On this model the emblem is more than just an emblem. it incorporates the radar module for collision avoidance and adaptive cruise control. That is one reason that the emblem is so large. It would be nice if it was a snap-in but I am not holding my breath.
Looks to me like the easiest way into the that area is to go from the top down. Looks like removing the assembly with the emblem will provide access to allow removal of a cover plate between the radiator and grille. Once this is gone you should be able to get your hands down in there.
Take a look at this thread in the General section. It's long but the first post has photos about how to replace the horns in a 2016 Rav4. I replaced the horns in my 2016 Limited but did not need to use the wood to open the area. I simply removed the top cover above the grill and released the two connectors on the left and right sides of the bumper (near the wheel well) and pulled the bumper forward to gain access. I had plenty of room to get to the horns. I think doing this will allow you room to reach the rear of the emblem to remove.