The first Akro corks were officially introduced in 1930, according to the earliest documentation I can find. It's possible that they were being made in 1929. However, the only styles I think possible at any time in 1929 were Prize Names, Onyx (including Cardinal Red) and Imperials.
Onyx and Imperials both appear in 1929 advertising, but it's not likely that they took corkscrew form yet.
The contest where Akro introduced their new line of marbles and invited children to help name them -- promising a prize to the best name -- was run in 1930.