It will not be in the ARP table until it has been pinged/contacted in some way... so...
If you have a Windows machine available and a little time, I would download angry ip scanner (version 2), set the options to the following:
(FYI, this was an old picture of mine... put threads to 1000! - if you find nothing or set this too high, your cpu may not be able to handle all the threads before the timeout is being hit.)
I would then hope I can guess the IP slightly... lets say I "think" the 192 range, I would change my machine's ip to 192.168.0.1, subnet 255.0.0.0, gateway/dns blank and put 192.168.0.2 - 192.168.255.255 as the ip range and start scanning.
Next, try 10.0.0.1 as your machines ip and scan to 10.255.255.255
This will take quite a bit of time, but, as long as ping isn't blocked on the machine - you are guaranteed this will work eventually.
You will have a single host listed when it is finished... and, all you need to do is ping the ip, followed by
arp -a - you will then have the mac address.
I know this isn't the fastest... pretty sure there is something you can do with nmap... but, that isn't my speciality and despite being slow, I guarantee this will work... have a few sessions open, you will be done in no time!