There is no dictionary meaning of the word "otherwise" as "already." A Google Ngrams search of the usage of "otherwise" for the years 1800–1820 does not reveal any examples of the word "otherwise" in that sense. (Click on the 1800–1820 option next to "Search in Google Books" under the graph.) Occam's razor therefore suggests that rather than Shelley's using the word in an idiosyncratic way, the interpretation of "otherwise" as "already" is mistaken.
A fuller contextualization of the sentence makes the meaning clear:
I paused when I reflected on the story that I had to tell. A being whom I myself had formed, and endued with life, had met me at midnight among the precipices of an inaccessible mountain. I remembered also the nervous fever with which I had been seized just at the time that I dated my creation, and which would give an air of delirium to a tale otherwise so utterly improbable. I well knew that if any other had communicated such a relation to me, I should have looked upon it as the ravings of insanity.
Frankenstein is planning to tell his family about the monster he has created. He realizes that the story is so improbable that he will not be believed. He also remembers that he had fallen ill with fever right around the time he created the monster. He says that his family will attribute his story to delirium caused by fever; otherwise, they will not be able to account for it.
In other words, "otherwise" here doesn't mean "already." It has one of its ordinary adverbial meanings, which Merriam-Webster defines as follows:
2 : in different circumstances
// might otherwise have left
// The test helps identify problems that might have otherwise gone unnoticed.
To his family, Frankenstein's feverish delirium would explain away why he thinks he created a monster. Delirium is the only plausible explanation. Otherwise, they would find no other probable explanation for his story, because his having actually created the monster is, to them, wildly improbable.