now u on the right way, u can set a value e.g. (PasswordSet) default this value is false,
now the user type in a password and now the password is set (true) then u can make a method "isPasswordSet" in the start of the application and this proof the value passwordSet. thats all.
the value u can set via the sharedpreferences, here is an example or answer how u realize that: How to use SharedPreferences in Android to store, fetch and edit values