What modem brand and model? Or could you take some pictures?
Nest Wifi main/ master puck requires an ethernet cable, RJ45, with access to internet to function. That's a hard requirement.
That's a desktop computer, not a modem. It can be connected to Nest Wifi by ethernet cable. If the one free port on the Nest Wifi router is not enough, you can add an unmanaged switch:
So either without an additional swich:
Or with an unmanaged switch: