There is no historical proof that the Buddha ever taught what people say he taught.
In fact, his teachings were not even written down until a century after he gave them,
some 5,000 miles south of where he spoke them, and in a language he didn't use.
So, there is no way to actually prove the teachings are true,
to your own satisfaction at least, except to test them out for yourself.
That is how we know Buddhism (the Dharma) is true.
What you describe is like rubbing two sticks together to make a fire.
We don't know who did that first, but we can replicate it, and that validates it.
There are historical reasons for most of the other issues you raise.
Buddha could have taught anywhere, of course.
And he might have. But "Buddha" is an Indian word,
and there were a lot of people in India who were listening to him.
So, like a popular song, it caught on. It went viral.
So, you know, maybe he taught in some other continents too,
but only 3 people listened to him,and that was the end of that.
We can make guesses. It doesn't really matter
because we can't prove it.
Even Buddha said (we think) that at some point even these teachings we have now
nobody will pay any attention to, or won't be able to grasp, and they will fade away.
If you look at history, most things happen within a social context.
They can only happen at a certain place and at a certain time in history because of the right conditions.
For example, what Andy Warhol did in the art world really could have not happened in the 1950s or earlier.
It could only happen in the 1960's, as part of it, and as part of what defined it.
So, we wouldn't think to ask,
"why wasn't Warhol silk screening soup cans during the Ming Dynasty in China?"
Because the conditions for that, except maybe for the silk, the pieces were not all there.
On the other hand, Chinese calligraphy is a great example of abstract art
which didn't happen in the west until the middle of the 20th century.
So, sometimes it all depends on how you look at it.
Buddhism teaches that all things arise interdependently.
"Searching for the truth" was, you might say, in style at the time of the Buddha.
A lot of concepts that appear in Buddhism, such as karma and rebirth, were already part of Hindu culture.
Likewise, in the days of Jesus, a lot of people claimed to be prophets of God.
So, that's when you have a big audience, and your message takes root.
Profile Picture: "The Foaming Monk"
The Chinese characters are Fo (buddha) and Ming (bright). The image is of a student of Buddhism, who, imagining himself to be a monk, and not understanding the true meaning of the words takes the sound of the words literally. Likewise, People on web forums sometime seem to be foaming at the mouth. Original painting by P.Volker /used by permission.