You have faith that the buddha wasn't lying
You have faith that the buddha was correct
You have faith that your methodology is correct
You have faith that the buddha knew enough to present something properly
The entire religion is faith.
No.
Buddha was not always correct - for all people. For example, he said 'Don't cotemplate about the creation of the universe. It will vex your mind and madden you'. I do not agree to that. It may be true for people who do not have the requisite background. But there are thousands of very knowledgeable who are trying to find the truth and million who understnd what conclusions they have arrived at till now. The problems do not madden them, but encourage them to go further deeper.
Buddha sure knew enough about what he was talking. His audience was 500 BCE rustic India. He, perhaps could not have talked in any other way. And what he said was a hundred times better than what people said later. For example, what he said to the Kalamas.
It is the original 'Occam's Razor'. He said:
"Do not go upon what has been acquired by
repeated hearing (anussava), nor upon
tradition (paramparā), nor upon
rumor (itikirā), nor upon
what is in a scripture (piṭaka-sampadāna), nor upon
surmise (takka-hetu), nor upon an
axiom (naya-hetu), nor upon
specious reasoning (ākāra-parivitakka), nor upon a bias towards a notion that has been
pondered over (diṭṭhi-nijjhān-akkh-antiyā), nor upon another's
seeming ability (bhabba-rūpatāya), nor upon the consideration,
The monk is our teacher (samaṇo no garū)."
Kalama Sutta - Wikipedia
World would be a much better place if we listen to what he said.