Did the Soviet Union ever officially admit it was racing to land a person on the Moon?

No. The Soviet crewed lunar program was never publicly acknowledged at the time, and its existence became widely documented only after the fact, which is part of why the United States could never be certain exactly how close a competitor it actually faced.

Why did the Soviets lose despite leading early with Sputnik and Gagarin?

Repeated failures of the Soviet N1 rocket, including a major test failure in 1969, meant the program could not deliver a crewed lunar landing capability before Apollo succeeded, regardless of its earlier milestones.

Was the Apollo program's cost unusual for a civilian program?

Yes. A budget share of around 4.4 percent of the entire federal budget for a single civilian program, sustained across multiple years, has no close modern equivalent in US government spending [VERIFIED].

science · 1961 to 1969

The Apollo Program: Winning a Race Fought in Secret

The Soviet Union never publicly admitted it was racing the United States to the Moon. That hidden uncertainty may be exactly what pushed NASA's budget, and its resolve, as high as it went.

Facts drawn from NASA's official history office and Encyclopaedia Britannica; interpretive framing is labeled as modeled analysis.

The Soviet Union's 1957 Sputnik satellite and Yuri Gagarin's 1961 flight as the first human in space shocked American political leadership, and President Kennedy responded in May 1961 with a speech to Congress committing the United States to landing a person on the Moon before the decade was out.

[VERIFIED] NASA's budget grew rapidly through the 1960s, peaking at around 4.4 percent of the total federal budget in fiscal year 1966, an extraordinary level of sustained resource commitment to a single civilian program, according to NASA's own historical budget records.

Play the same structure: The Moonshot Budget.

Sources

[VERIFIED] NASA's budget peaked at around 4.4 percent of the federal budget in fiscal year 1966 NASA History Office, Apollo Program Budget Appropriations, SP-4029
[VERIFIED] The Apollo 11 mission and its July 20, 1969 lunar landing NASA, Apollo 11 mission overview
[VERIFIED] The broader Cold War space race context, including Sputnik and the Soviet program's secrecy Encyclopaedia Britannica, space race