Greyed out port for Raspberry pico in Arduino IDE - Ubuntu 20.04
I've come across this and this is how I worked around it (on Windows, but I suspect the problem and solution is the same).
A brand new Pico or one not programmed by the Arduino IDE does not have a serial port, which is why you can't see one. Arduino sketches are compiled with a serial port automatically, so once a serial port exists, it can be used for future uploads.
The Arduino solution is to use the 'Export compiled binary' option (for any sketch) and upload the UF2 file (which should be generated into the sketch folder) using virtual USB drive interface. When the sketch starts, the serial port will be available and can be used for future sketch uploads.
Another solution is to use an alternative Pico core. This one does not need the port selected, but will find and upload to a Pico in bootloader mode via the virtual USB drive.