What it says on the tin. What's the earliest date that they could have laid a transatlantic telegraph cable that would've functioned for at least a few years before failing?
In addition to the ship you needed to have a water proof covering strong enough to survive on the floor of the Adlantic. This basically meant the rubber derivative they used.
Since this needed rubber plantations + advanced chemisty I would have said that it was an idea which could not have happened much before it did.
Underwater cables were made of guta percha, and did not require advanced chemistry. The stuff had been used by native Malays for God knows how long and commercialized in Europe in the 1840s.