Final answer:
The sentence where Kennedy proposes to Congress "that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to Earth," most supports the notion of a specific target in the space race against the Soviets.
Step-by-step explanation:
The sentence from President Kennedy's speech that most supports the statement that the "space race with the Soviets finally had a specific target" is found in his address to Congress where he states: "that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to Earth." This decisive goal-setting came after the Soviets achieved the first human orbit of Earth by Yuri Gagarin and reflects the strategic target Kennedy set to surpass Soviet achievements in space.
In his commitment to landing an American on the moon, Kennedy was responding specifically to the Soviets' earlier achievements in space exploration. This goal, set on May 25, 1961, became a pivotal focus of the U.S. space program under NASA, and was eventually realized with the Apollo 11 moon landing in 1969, marking a significant milestone in the Cold War space race.