Dear Putran ji,
You have raised a valid point. In this context, an analogy would help clarify the matter stated in the Book. Most of us have experienced instances where a familiar song or story offers new insights upon hearing it again. Reading a topic multiple times reveals fresh understanding. Many stalwarts in the Shankara Bhashya have attested to this. A similar scenario applies here. Even though the aspirant is familiar with Vedantic methods, the Mahavakya, and how it works, persistent study and contemplation can lead to a crucial understanding of the Atman. This one stands out as unique, especially considering the several rounds of study and contemplation done before. Through sincere contemplative practice, the aspirant has matured enough to now see a hitherto unknown/unseen meaning in the Vedantic teaching, especially the Mahavakya. This can be termed the Mahavakya producing in him the liberating understanding the moment he hears it this time—say, from a recorded speech—recalls it or utters it as part of his routine spiritual practice. It can be likened to the Eureka moment.
We do have experience like, "I had heard it several times before but this time it was as though I was hearing it for the first time."'
Even according to the cited lines (from the book), there is an a priori requirement that the aspirant knows the meaning of Tat, Tvam, and Asi. Only under this condition can the mahavakya, when heard, produce the intended result. We may also keep in mind that the mahavakya can take many different forms. The Vedic corpus itself contains several, and Bhagavatpada attested to many of them, though he did not use the term in the PTB.
Warm regards
subbu