This types of pans and drains leak all the time.
Often the daily flexing in the pan at the drain connection will stress and then fail this connection.
Any type of quick fix will only mask the problem short term.
Replacing that connection and all the work that comes with it is your best approach. This way you can inspect the damage the water has done to date and get back to a proper shower.
As for quick fixes. Kerdi Fix is an "Uber" sealant that would make a waterproof seal. It is not designed to be left exposed and untiled but would most likely give you a good short term band aid.