How to repair sub-floor in popout

Hello all, I have a supper soft spot in the flooring material of the popout. When you step/stand on it feels like you will fall thru. There are no signs of water damage. The carpet is dry. It has been said that a dealer will want $3000 to repair. I'm not looking forward to doing it myself, but I'm fully retired and so I'm the repairman.

Any advice will be greatly appreciated.