After pulling my hair with Sparsha´s amazing firebase Plugin, there are two main things that cause a black screen (had the same problem many times)
Please notice I´m not an expert, just had the same problem many times.
Check:
1. Worker mode is disabled
2. You need to tell FirebaseAuth, firebaseAuthpro, FirebaseRdBasic, etc under properties, Choose SDK Object and select FirebaseSDK
This 2nd option it´s always a thing for me, I keep forgetting linking them
Hope that solves your black screen, If not, I´d suggest you to ask in Sparha´s Construct Firebase Discord chanel listed with the files downloaded with your plugins.
Everyone there is super helpful, specially sparsha, who I cannot thank enough one time I had a similar problem, he gives an amazing support :)