Its current tranquil beauty gives no hint to its recent run-down state nor to the great effort needed to restore it. According to the owner, Ku, "El Patio del Cielo is proof that, through determination, on can fulfill any dream."


Could I replace the bolded part with "is living proof that" or "proves that" without making a change in meaning? Thanks.
"is living proof that": NO, because it must refer to living things, which a restaurant isn't.
"proves that: yes
If you want to stress that this example (restaurant as I understood) is the best and actual proof of the aforementioned rule, you can say that it "clearly" or "definitely" proves that rule.