With the resources I have available to me I have been able to trace the expression
papa spank [sometimes written as pappa spank and papa spanks] as far back as 1911 Boston. But even at that time we can tell that the phrase is already a well-known blurb, a saying that had it remained relevant into the 1970s would have been on bumper-stickers nation wide.
Newton Newkirk writes a humor column for the Boston Post in 1911. He receives a whimsical question from reader Claribel and jokingly rebukes her as a mischief maker going so far as to threaten her with the words, "if you don't be good papa spank". Mr. Newkirk has no intention of actually spanking Claribel and he is not her "papa" but he knows there is humor in using that phrase that will immediately be understood by his readers.

- PapaSpankNovember18,1911BostonPost_LI.jpg (748.8 KiB) Viewed 3954 times
We're trying to determine the origin of the catchphrase
papa spank made iconic in Batman #1. From where did Mr. Newkirk grab this phrase? Social media and in fact mass media was quite different in 1911 than what we are familiar with today. Popular entertainments of the pre-WW1 years included magazines, books, wild-west shows, minstrel shows, plays, stage musicals, lecture tours, early silent movies, burlesque and vaudeville. I can't argue against any of these media as being the source of the papa spank slogan but if I had to make an "educated" guess I would point us towards vaudeville as being the probable place of origin. Vaudeville was the name for a popular form of entertainment that offered a live, staged variety show that toured city to city over the course of a season. Vaudeville originated in the 19th century and an evening of vaudeville could include sketch comedy, singing, dancing, juggling [that's how W.C. Fields started] and numerous novelty acts. Vaudeville was known to be very popular in Boston in 1911. Over the course of the first decades of the 20th century we have ample evidence that the term papa spank was a popular vaudeville expression.
For example in June 1921 a vaudeville show came to Bedford, Indiana...

- PapaSpankJune2,1921BedfordIndiana_LI.jpg (1.03 MiB) Viewed 3954 times
A vaudeville advertisement from Christmas Eve 1920

- PapaSpanksDecember24,1920HamiltonDailyNews_LI.jpg (1.1 MiB) Viewed 3954 times
Now for sure the two words
papa and spank could be found sequentially in a sentence long before they became a meme predecessor.
For example we might have this -
"Susan did papa spank you for taking the buggy out without permission?" "Of course sis, you know papa spanks hard with his razor strap when we misbehavior even though we're out of school." But at some point the small phrase was grabbed by presumably a late nineteenth, early 20th century performer or performers and made famous for decades to come.
If you know anything specific about the origin of the catchphrase papa spank please let me know. Let's see how popular that phrase was by 1940 and why it wasn't at all an out of the ordinary turn of phrase as used by Bob Kane in Batman #1.