When the Nineteenth Amendment passed, while women were able to vote, that does not mean they were immediately turning out in large numbers.
For one thing, women had to be able to register to vote, and there were barriers to that, like poll taxes and literacy tests. Black women in particular suffered in that respect; for example, in Columbia, South Carolina, over a hundred black women arrived to register in September 1920, and the registrars stalled to have the white women registered first. The women had to return the next day and then got stalled by the literacy test being pulled from the legal code (not the Constitution, as it was supposed to be); the women were unilaterality told they failed the test no matter what the results.
There was also a legal challenge, as Mary Randolph (who was black) and Cecilia Waters (who was white) both registered to vote in Baltimore, and had their registration challenged in Leser v. Garnett. The claim of those suing was that the amendment was not properly ratified, and while the Supreme Court decision was unanimous, this still understandably contributed to a general atmosphere of trying to keep women from voting. Another lawsuit attempting the same, Fairchild v. Hughes, saw a private citizen (Fairchild) try a "public right" suit; the Supreme Court decided since the suit came from a place where suffrage was already allowed, the claimant had no standing (this term wasn't used exactly -- this was in fact one of the earliest uses of the concept).
Adjoining these more overt tactics is the simple fact of inertia: women who had never voted before were not used to going out and voting. The League of Women Voters (established in 1920 out of older suffrage groups) set out with a mission of education and to bolster the women's vote. They gave out encouraging material and made demonstrations on the actual skills involved in casting a vote (like how to fill a ballot).
The turnout was poor enough -- 33% in 1920, and not much greater after -- that the question Is suffrage a failure? was openly asked in magazines. Some pounced on the opportunity to characterize women as inherently apolitical.
This political cartoon is from 1926 ("Let's see, what was it I was going to do when I got into politics?"). The Women Citizen responded with commentary:
The artist must have remembered certain glib cure-alls unwisely offered by some of the stump speakers in the campaign for full citizenship ... he has related those problems to the women voter. In his estimation she has fallen down on them.
1926 is also the year, in Texas, where there was:
...an elaborately planned campaign to get out the vote, under the direction of Miss Mary E. Jagoe, president [of the League of Women Voters]. "Go to the polls and take one voter with you" was the slogan. Local Leagues utilized every available agency to increase the number of voters participating in two very interesting primary elections. It was the first time that a Republican primary had been held in Texas.
Posters were distributed; ballot marking classes were conducted; and some thirty-five slogans, drafted by Miss Jagoe, caught the eye of voters in buses, street cars, shop windows and manufacturing plants. "I have voted" tags given out at election booths stimulated last minute voting.
This is one of the earliest mentions we have record of; while stickers could have shown up earlier in the 1920s, they were more or less exclusively linked to the League of Women Voters up until WWII. Post-WWII, they became more normalized; a 1950 article in Miami mentions "I have voted" stickers, and fairly consistent references can be seen after.
The specific design often seen has more to do with capitalism than women's rights. The sticker was designed by Janet Boudreau in 1987 while working for the company Intab, which sold (and still sells) election supplies. Stickers from earlier in the 80s tended to have checkmarks or Xs, an increasingly irrelevant graphic in an era with punch cards. According to Boudreau herself:
Rather than copy what was out there already, I wanted to improve it, make it more applicable to any voting system.
Hence, her design of pairing "I voted" with a flag. It is still copyrighted under the one company. Intab currently sells more than 30 million of the stickers a year.
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You can see a chart here of percentage turnout in the early years of women's voting. The jump in 1928 is generally thought to be because Al Smith, a prominent "wet" and Roman Catholic, was running for President, and Prohibition and religion were strong motivating forces.
Fitzpatrick, E. F., Flexner, E. (2020). Century of Struggle: The Woman’s Rights Movement in the United States, Enlarged Edition. Cambridge University Press.
Johnson, J. M. (2022). The Woman Suffrage Movement in the United States. United Kingdom: Taylor & Francis.
