It is possible to add a glass bed and get the levelling to function with it, yes. The levelling sensor triggers on metals, like the layer of spring steel sandwiched into the default print bed. Easiest method to level with glass is to put the default print bed on top of the glass—that won’t be perfectly level if you print with them in that configuration, but it will be much closer. Or you can place a metallic object on each point as it’s probed. For a more elaborate and automated solution, ask around and see if anyone has the files for the FiFix handy.
Do double-check how you assembled your bed first, though, as some people have discovered their really poor levelling is due to parts having been installed upside-down or the like. 
Relevant threads about levelling on glass (be warned that they’re long):
https://forum.snapmaker.com/t/a350-printing-on-glass/5238/
https://forum.snapmaker.com/t/for-all-who-want-level-on-glass/12437