The first realistic opportunity came in June 1959, but neither of the two space powers at the time had the means to send a vehicle to Venus. The Moon itself is still in sight. The second takes place in February 1961, but NASA faces so many problems in the months before with its lunar missions, which fail because of the launchers, that no attempt can take place.
However, the USSR tried it. It provides for two take-offs of impactor vehicles only a week apart, with an identical design and the same mission. Foresight paid off, as the first of two shots failed during the last phase of the launch, and the probe remained stuck in low orbit. The second attempt was successful and the Soviets named it Venera-1. The probe is even the first to fly over Venus… Well, maybe. Indeed, at about 100,000 km from the goal, the earth stations lose contact.
A very relative mission success, therefore, since it brings nothing if not a lot of lessons for the next attempt.