WHY does one believe, that he was totally free from misery or mental anguish?
Perhaps you can see the "Noble Truths" in your own life -- suffering, cause of suffering, cessation of suffering.
Given those are true, based on your own personal experience, perhaps it's not too hard, perhaps it's plausible, to imagine that someone (the Buddha) who ...
OP: Here is the problem: we know that the Buddha suffered hardship in this world, including sickness and requiring a physician at times.
We know that he had enemies who wished him harm. How then is it
possible to believe that the Buddha was the happiest or most fortunate
person ever to exist? Surely, out of all of history, with billions of
people, there must ...
Well first putthujjanas won't know anything about the dhamma until they become at least sotapanna. Until this, all puthujjanas have is believes and doubt. It's completely normal.
All the puthujjanas can do is cultivate what the buddha recommend to be cultivated, that is the 8 fold path. This is pretty hard for anybody. It's worse when there is no buddha.