I was looking around on the Wikipedia page for the real-life Tokugawa, and a reference to New Spain put me into a little bit of a wikipedia link rabbit hole.
Anyway, after reading some links I'm picking up on what might be a pretty big historical inaccuracy that would throw off the shows plot.
Apparently, in 1583 (almost 20 years before the show is set), Japanese ambassadors had already gone on a major multi-country tour of Europe:
Tenshō embassy - Wikipedia
It's pretty important to the plot that the Japanese leadership thinks that "Portugal = Europe", but apparently in real life that was not the case at all.
Of course, for THE SHOW it doesn't matter all that much, since its a TV show and not an actual history lesson.
Basically, James Clavell needed to come up with a plot point to make Blackthorne more important than he would have been in real life
The show is based on a book that itself was historical fiction.
Its not meant to be 100% accurate to the time period