When you state that the only way to connect to the machine is via SSH it implies that the machine has either a known IP (which you do not know) or a known name. If that is so, just resolve the name:
I am giving the example with dig (and it may also be
dig +short name), but many other tools are available, like getent, ip, nslookup, host and many more
If the above is not a solution for your case, then: When you state:
physically connected to my network
Does it mean that the computer is able to communicate with other computers on your network or the internet?
If yes, then it must have an IP (either IPv4 or IPv6).
You can scan at level 3 (IP level) with (similar to)
nmap -sn 192.168.1.1/24 as an user. The command example will only scan the
xxx.yyy.1.zzz segment. For all segments (as you state that you only know the
192.168 prefix) you will need to use (very very slow, more than 1 hour ), note the trailing
nmap -sn 192.168.1.1/16
If you have root access, nmap could execute an ARP scan (faster but still in the hour range) with the same command, or, you can install and try (about 2 minutes 13 seconds for 65536 IPs with default network speed):
Or, if you must specify the network segment:
apr-scan 192.168.11.11/16 or similar.
There is NO practical way to scan a local network for existing computers in a reasonable time. The fe80::/64 has 264 IPs, that's 248 (281.474.976.710.656) times the
192.168.x.y range (well, technically the range is fe80::/10, but it must be followed by 54 zeros, so, that's equivalent to the /64). And that is just one of the possible IP ranges an interface could have (interfaces are multihomed).
But, there is a command to find the neighbors (that have been active):
ip -6 neigh