The earliest reference I know about is

[Wendt, H. Die gordische Auflösung von Knoten. Math. Z. 42, 680–696 (1937)][1]

It's been a very long time since I read this paper (and my German is mediocre, so it would take some effort for me to re-read it today), so I can't remember if it references anything else.

As evidence that this is the original source, Reidemeister's classic [book][2] on the subject references Wendt's paper when it introduces the unknotting number.  See the beginning of Chapter 2.


  [1]: https://link.springer.com/article/10.1007/BF01160103
  [2]: https://www.maths.ed.ac.uk/~v1ranick/papers/reidemeister_eng.pdf