Flex bit for drilling down through subfloor. Take it slow and easy. Hit a snag, stop and back out and move over a bit. Knots in the wood will destroy these things. Use razor blade and/or drywall knife to knock out wall plate size hole. Plenty big enough to put flexbit through. Used this many many times running AV cabling
Irwin Tools 1890759 Flex Shank Installer Drill Bit with Auger Tip, 3/4-Inch Shank, 54-Inch Length https://www.amazon.com/dp/B00LLGT4GI/ref=cm_sw_r_cp_apa_dp8CAbDY3MD5J
IS the drywall/plastic the side where the TV is mounted? Kind of hard to get a perspective from how the picture is.
If so that cross 2 x 4 makes sense, builders will install bracing to help reinforce TV mounting, to make installing wall mounts easier.
If you want to reach it and drill through it, you need to get a long flexible drill bit like this https://www.amazon.com/Irwin-Tools-1890759-Installer-54-Inch/dp/B00LLGT4GI that'll help get you the angle and distance you need to drill through it, its also great for pulling wire through those drilled holes as well.