The doctrine of Transubstantiation explains, to the best of human reason,
how the change happens.
That the change happens is something believed by pretty much all non-Protestant churches, from the Assyrian Church of the East, to the Armenian Orthodox Church, to the Tewahedo Orthodox Church of Ethiopia. These other churches may not have the Aristotelian understanding of accidents and essence/substance of things, but they
do profess that the change happens, they
do have validly consecrated bishops that go back through an unbroken line to one of Christ’s Apostles, and since their sacraments are valid, the change
really does happen in their liturgies.
Thing is, the earliest Christians seemed to understand that Christ was speaking of Peter and the subsequent See established in Rome.