Did you install XQuartz from
https://www.xquartz.org
or from another source?
Did you reboot your Mac, after installing XQuartz so that it establishes all the correct hooks into your logging GUI environment?
I never have to manually start. I either start a local X11 based app (/opt/X11/bin/xclock or /opt/X11/bin/xterm for example), or I
ssh -Y user@remote.Linux.system
and start an X11 based app on the Linux system
If I really want to start manually, I can double click on the XQuartz icon, but I never do that, as mentioned above, it automatically starts when an X11 based app starts talking to the port established by the DISPLAY environment variable.
And you are going to have to reboot (or logout and login to your macOS session) at least once after installing XQuartz so that the DISPLAY environment variable is established, an so that the ssh -Y command can create a proper X11 tunnel.