Really being Buddhist does not require an act of faith?

For what is my understanding of Buddhism, the Buddha teachings aim to solve the problem of suffering. The buddha said you don't have to have faith in him or his teachings that you will be liberated from suffering, but you are encouraged to try it yourself and experiment the results. At the same time, you might need several lives to obtain liberation, isn't this equivalent to an act of faith? From the perspective of a person who is approaching Buddhism for the first time, you ask them to put a lot of effort and time on something it is not verifiable. Kinda like christianity, if you behave according to the christian commandments you will go to heaven, I feel like they are the same concept. Also during my researches I have found in Buddhism teachings there are a lot of analogies that are quite charming, but if you think about it carefully they are not quite correct. The one I have met the most is the analogy between the Four noble Truth and a medical treatment. Regarding the treatment part in particular, I think a medical treatment is a very precise and deterministic series of steps. You follow the steps and you get a precise result in more or less precise period of time. The Noble Eightfold path instead, I find it very vague, a lot of concept are explained with "it can't be comprehended with concepts and logic". Doesn't this also require an act of faith? To people who are practicing Buddhism, have you done an act of faith when you approached Buddhism for the first time?