The only other dates I’ve found have been much later.
“Russian composer Tchaikovsky included the accordion in his ‘Suite no. 2’ (C Major, op 53), as did Prokofiev in the ‘Cantata for the 20th anniversary of the October Revolution’”
Who would have thought it was an orchestral instrument?
I think for the purposes of popular familiarity, they originated at about the same time. The polka was introduced to Paris around 1840 (as you note), but it was an adaptation of a Bohemian folk dance, so it could have been much older.
The word accordion entered English in 1831, putting it earlier than the introduction of the polka to Paris society, and it probably was a bit older in Germany.
I was also surprised at the dearth of accordion history that is out there. It does not seem to have become a really popular instrument until the 1880’s or 1890’s, so the polka would have priority from that perspective.
My copy of the OED [Oxford English Dictionary] says Accordion … A portable musical hand-instrument invented in 1829 by Damian at Vienna. So clearly it came first.
1829 clearly beats the 1840 introduction of the polka to society in Paris.
(Of course, if the Bohemians were calling their wedding dances polkas in the 1740’s (or 1640’s ) or earlier and they only made it out of Bohemia in 1840, that would indicate a different order of precedence. I do not actually know when the Bohemians first danced the polka, but I suspect that a “folk dance” that was brought to Paris would have developed earlier than its first choreagraph in Paris. On the other hand, for the purpose of this discussion, the accordion is the clear winner.)