The effects of granting suffrage tended not to cause quite as large an increase in ballots cast as you expect.

For example, the US presidential election of 1920 was the first after the 20th amendment, but the ballot increase from the 1916 election was 18 million votes to 25 million votes. (This partly because 30 states already let women vote.)

New ballots are printed for each election anyways. It just becomes a matter of calling the printer in time.