There's a nugget of conventional wisdom that most timelines have a more successful space program than ours. But how realistic is this, actually? Or, to ask more precisely (and with more focus):
With a POD after the return of the Apollo 11 mission to Earth, what is the probability that a human would walk on the Moon at some point in the period 2001-2010?
Realistically, only two programs have a significant chance of being able to go to the Moon between 1970 and 2010 (I assume you would be fine with a return to the Moon in the '80s or '90s), NASA and the Soviet program. However, the latter was in a funk for most of the '70s, was consumed by developing the Buran/Energia combo during the rest of the '70s and the '80s, and then kinda disintegrated with the USSR, so they're less capable of doing so than the US. A surviving USSR with the Energia/Buran combo would be relatively able and likely to do so, however, since they have a high-performance launch vehicle which has neatly sidestepped the problem with most SDLV proposals ($$$) and a reason to actually launch a mission (pissing on the US, more or less).
Now then. For the American program, the best way forward is to kill the Shuttle before it's approved by the White House, say in 1970. While I like the idea of the Shuttle and think the thing is cool, there's no way around the fact that (despite the substantial theoretical potential of the components) it effectively retarded the US space program for 40 years and limited it to LEO-only missions. It was not as cheap as was hoped due to unforeseen limitations in a variety of areas (and the over-optimism of NASA's leaders), and in any event has sucked up a huge amount of cash since it's beginning, inhibiting other worthy programs. Despite some very clever later planning by NASA people, it didn't really have the ability to launch a lunar mission without on-orbit assembly and probably fuel depots, which would basically need NASA to build the first version(s) of
Freedom...which cost too much money and so kept getting canceled by Congress (ironically increasing the cost, but I digress). Even then, propellant launches would be too expensive (and way too dangerous under post-
Challenger safety rules) to put on the Shuttle, so it would need multiple supporting expendable vehicle launches to actually do a mission. With those limitations, which would you rather have: a Shuttle that costs as much or more than most expendable launch vehicles (and needs some to actually do the lunar mission) to launch a mere 20-30 tons into space (needing, BTW, a crew of 4-7 on board for any flight, even a totally routine satellite launch or fuel delivery), or...the expendable launch vehicle with the same payload and the same or lower ongoing costs, and a much lower development cost, but man-rated and able to carry a capsule with 3-6 people into space? Canceling the Shuttle would save NASA quite a lot in development and maintenance costs (especially if they use the Titans, which are supported by the Air Force as well, maybe convincing them to do it by scheduling a couple of "Blue Apollo" missions), which would be very useful for developing the technologies needed for going back to the Moon.
Fundamentally, though, the problem is that put forward by SunilTanna: Going to the Moon is expensive, for a dubious return, and would take a while for any country to develop the needed hardware from the word "Go". Additionally, most people don't really care about the Moon or space exploration; they like the pretty pictures from Hubble or Spitzer or Kepler finding other Earths or whatever, but they neither want to increase nor decrease the budget of your space agency of choice. So the only way to go back to the Moon is to make it cheap enough and easy enough with what you have that it's not that big a deal, budget-wise. That means things like fuel depots, medium-life vehicles, and so on, and a great deal of, essentially, infrastructure development, before any trans-Earth missions. It's boring, but any other way is likely to end up like Apollo: Quick, cool, and canceled after the first couple of flights when politicians realize they're spending loads of cash for no return and can score some cheap political points by not going to a place no one (in relative terms) cares about.
@Thande: NASA planners probably invented something similar back in the '80s or '90s...you should look as astronautix or
this NSS list of '90s lunar base proposals. You'll note the one I linked you to has some startling similarities to Constellation...you should look up the guy who was in charge of the Office of Exploration back then...