You don't need to solve the halting problem to prevent such access, not even close. You simply apply the same strategy as any other property you want to enforce - you prevent any use of the variable that can't be proven safe. You want to pass this in a call from the constructor to a function defined somewhere else where it might access a final/non-null able field that has not yet been initialized? Not allowed, only member functions that don't call other non-member functions allowed from the constructor.

Of course, as I said, this ship has long sailed for general Java classes. It would be far too big of a breaking change to add such a limitation today. However, we know for sure this could have been done in Java: this is exactly how record and now value classes work: any call that could expose un initialized fields is in fact disallowed.