According to this ngram, the phrase dates back at least to the middle 1800s, and usage to convey the inexplicable can be found in numerous examples around the turn of the century, for example
But it was just one of those things which occasionally come to pass ...
The Grey Monk in The Argosy, Volume 57 (1894), edited by Charles W. Wood
I suppose it is just one of those things which happen.
The Ambassador: A Comedy in Four Acts (1898) by John Oliver Hobbes
We do not understand it, and are apt to dismiss it as "just one of those things." In these lessons we are attempting to explain some of "those things," and to enable you to use them consciously and understandingly, instead of by chance ...
A Series of Lessons in Raja Yoga (1906) by Yogi Ramacharaka, William Walker Atkinson
Don't you think I'm blamin' you, Jim. It's just one of those things that's got to be.
The Call of the Hills (in The Black Cat, Volume 11) (1905) by Lucretia Dunham Clapp
I have no reason to give. I do not think that there is any willful intention to do anything wrong on the part of the Government or the Commission. I think it is just one of those things that happen, possibly, with a number of officers in different lines, ...
Investigation of Panama Canal Matters: Hearings Before the ..., Volume 4 (1907)
There are a few earlier examples that seem to convey something similar, such as
If we might be permitted to quote from Dundreary, we should tell you that who St. George was and what he did is “just one of those things that no fellah can find out."
New Outlook, Volume 10, (1874) edited by Alfred Emanuel Smith, Francis Walton