The argument mapping community generally deems the first occurrence of argument mapping to be in Richard Whately’s Elements of Logic textbook, first published in 1826. (See e.g. Reed, C., Walton, D. & Macagno, F. (2007) “Argument diagramming in logic, law and artificial intelligence”, Knowledge Engineering Review, 22 (1), pp87-109; p.93.)
To me it is implausible that there are no earlier examples, but I cannot point to any, despite having “kept an eye out” for a number of years.
Here, for the record, is that earliest occurrence:
This is the only diagram in Whately’s Elements of Logic which is close to an argument map. Note that it is an argument map schema or template rather than an argument map. Whately’s comment “Many students probably will find it a very clear and convenient mode of exhibiting the logical analysis of a course of argument, to draw it out in the form of a Tree, or Logical Division” suggests that the practice of argument mapping did exist at that time.