What's the origin of the phrase "bubble gum and shoe strings"

There are different versions such as “string and chewing-gum ” or “bubblegum and shoelaces”. The origin is probably just from common sense knowledge of two items that suggest a precarious and unreliable solution.

There’s an old saying about something being held together by just string (or shoestrings) and chewing gum. The idea, of course, is it is not a reliable (or solid) state of affairs. As things go, yours truly often has the notion that life is being held together with string and chewing gum.

(carpathianpeasant.wordpress.com)

An early usage example is from 1924 as suggested by user Gregor Y:

Fom The Northeastern Reporter, Volume 140

In this precinct, for want of a wire on which to string the ballots, they stacked them in piles after they were counted, and tied them, thus piled, with strings two ways and sealed the strings with chewing gum where the knots crossed, and then put ...

From The Address of Mr. Hachiro Arita, Minister for Foreign Affairs, at the 70th Session of the Imperial Diet, January 21, 1937

Some people suspect that the American economic system has been put together with string and chewing gum and that its greatest characteristic is its lack of system .