Can I repurpose this RJ45 setup for phone to run as Ethernet?

So my home is wired with what I thought looked like Ethernet ports. After trial of plugging in my computer and seeing that the ports weren't working as Ethernet cables, I dug deeper.

The wires that run throughout the house are all cat5e. My router is hooked up in the living room with an Ethernet cable running from the ONT port on the back of it to a port in the wall named 1A. Right next to 1A sits a port named 1B. all of these cables run to a central hub in the master bedroom closet.

after finding this hub I realized that all the Ethernet cables running throughout the house are connected to a telephone line switch. and above that switch is a small white box with AT&T on it that one Ethernet cord is plugged into (I'm guessing that's connected to the port that my router is connected to). If I wanted to run a few of these cords that are connected to the telephone hub as Ethernet to the rooms, is the fix as easy as buying an Ethernet switch, unplugging the cables from the telephone switch and plugging them into the new switch, and connecting the Ethernet switch to the small white box i talked about previously?