In September 1964 Bertrand Russell published Sixteen Questions on the Kennedy Assassination. I'm sure there were some earlier instances but that's one example from less than a year after.

http://www.personal.kent.edu/~rmuhamma/Philosophy/RBwritings/sixteenQues.htm

While not specifically a reference to the emergence of the very earliest of the JFK conspiracy theories, doubts as to the official accounts was mainstream enough that CBS televised a recreation of the shot that Oswald took in 1967.

[YouTube] JFK Assassination Oswald CBS Mannlicher Carcano Rifle Test 1967

I think it is worth mentioning that the test was relatively successful in their attempts.

Sort of revelant question: were previous assassinations, both within the U.S. and elsewhere, subject to the same type of speculation? Did conspiracy theories pop up as a result of, say, the McKinley assassination?

Question: I just got here, what's up with all the removed comments? There's 9 removed from what I'm seeing here, and only one comment has been left up. Wassup, admins?

Also, all the information I'm finding is pointing to /u/ricksplace's comment being correct. There were theories, obviously, before Bertrand Russel's publishing of them (otherwise he'd have had nothing to publish...), but that seemed to be the first widely-viewed and well-received publishing.

A reiteration of the link provided if you somehow missed the top comment from /u/ricksplace