Good news is your cables are labeled. Notice the number bands on each cable. You need to determine which cable goes where. Start by taking the wall plate off one of the ethernet ports. Hopefully that end of the cable has a corresponding number. Once you have mapped all the cables you can start moving them. UNPLUG the cable closest to the router. Run a patch cable from the router to that wall plate. Then connect the other end of the cable to an ethenet switch. You have an AC plug there to power the switch. Then other cables can be connected to the switch to distribute the network.
I looked at your picture again. There are a few cables which are not connected to the telephone block. If you are lucky you can use those cables.
When dealing with in-wall cabling, I recommend you have a simple cable tester like this --
https://www.amazon.com/Klein-VDV526-052-Scout-Junior-Tester/dp/B004CI9NRM It includes a "remote" You can plug that into a cable in the box and go around to wall plates until you get a match.