The parcel appears to have been opened before it was delivered.
Could you let me know if it is possible to use 'to be opened' instead of 'to have been opened', and if not, why?
A past event that happens before another past event.
"The parcel appears to be opened" can only be understood as the present tense, and adding "... before it was revealed" cannot override this, it can only create confusion. The main verb "appears" is in the present, therefore "be opened" is also in the present, and nothing can shift it into the past.
Therefore you must say "The parcel appears to have been opened before it was revealed" - here the main verb "appears" is still in the present tense, and "have been opened" is also in the present tense, but because it's Present Progressive, the opening itself can be thought of as happening in the past, and "before it was revealed" works well.
You contrast this with "the parcel was opened/had been opened before it was revealed". Here the situation is different because "was opened" is already in the past tense; "had been opened" places it in the correct time with respect to "was revealed", but in common usage it's fine to say with the simple past "was opened" and let "before" provide the context.