"NASA, the Moon program , were created in reaction to the Soviets initiatives in space."

Of course the people actually first with initiatives regarding space were American. And the Soviet effort regarding space was to beat the American efforts regarding space.*

But yes, NASA, the govt agency, was created as a reaction to the Soviet putting the first satellite in orbit, etc.

A significant difference between American and Soviet efforts in this regard was that America efforts were published and Soviets kept their plans secret. And what was published by Soviet propagandists were the successful completion- not planning and all the failures.

* "Following a suggestion by NAS member Lloyd Berkner, the International Council of Scientific Unions in 1952 proposed a comprehensive series of global geophysical activities to span the period July 1957-December 1958.
....
International organization and funding of the IGY were overseen by the International Council of Scientific Unions (ICSU), an independent federation of international scientific unions. A Special Committee for the IGY (CSAGI, an acronym derived from the French) was formed to act as the governing body for all IGY activities. Care had been taken to ensure that CSAGI would remain nonnationalistic, apolitical, and geared toward a scientific agenda.

American participation in the IGY was charged to a US National Committee (USNC) appointed in March 1953 by the NAS. Joseph Kaplan, Professor of Physics at UCLA, was appointed Chairman of the USNC. Physicist Alan H. Shapley of the National Bureau of Standards (NBS) was appointed Vice-Chairman, and Hugh Odishaw, also of the NBS, was appointed Executive Secretary (later, Executive Director). The core USNC was made up of sixteen members, but the five Working Groups and thirteen Technical Panels that operated under it eventually drew in nearly 200 additional scientists. The technical panels were formed to pursue work in the following areas: aurora and airglow, cosmic rays, geomagnetism, glaciology, gravity, ionospheric physics, longitude and latitude determination, meteorology, oceanography, rocketry, seismology, and solar activity. In addition, a technical panel was set up to attempt to launch an artificial satellite into orbit around the earth."
http://www.nationalacademies.org/history/igy/

Of course, much earlier than this the Germans made to V-2- which traveled suborbitally with large warhead. With some modification of this technology it could allow small objects to be put into orbit. [And the V-2 technology was captured by both American and Soviets.]

And there was the X-15 program- which was approach to getting into space which preceded SpaceShipOne.

In my view, in an alternative reality without the German V-2, America would have went to space the "right way"- via the X-15 with follow on programs.

"The X-15 was based on a concept study from Walter Dornberger for the NACA for a hypersonic research aircraft. The requests for proposal were published on 30 December 1954 for the airframe and on 4 February 1955 for the rocket engine. The X-15 was built by two manufacturers: North American Aviation was contracted for the airframe in November 1955, and Reaction Motors was contracted for building the engines in 1956.

The first X-15 flight was an unpowered test flight by Scott Crossfield, on 8 June 1959; he also piloted the first powered flight, on 17 September 1959, with his first XLR-99 flight on 15 November 1960."
http://en.wikipedia.org/wiki/North_American_X-15