The only thing I can think of for now is creating a small FAT image file and mounting it to /sdcard. But this assumes you have the privilege to do this, which is a slightly dangerous assumption.
If you have access to init.d or userinit.d, etc. a small script to check for the existence of said image and create and mount it (or, repair the mount) could be whipped up in seconds, but this might be overkill.
It really bothers me that /sdcard doesn't exist at all. Even if it does just point to /storage/*...what device is this?