After trying it out in Kerbal Space Program for a while, I was wondering why NASA doesn't fly on suborbital trajectories to the Moon. When I tested this idea in Kerbal Space Program I found out that you would save fuel, time and money by building a rocket that would fly to the Moon. The flight would take about 20 hours instead of 3 to 7 days and the rocket would have 2 stages, but I did manage to do it with a single staged rocket. The first stage would separate and then land with a parachute, while the second stage would go on to fly to the Moon. I have done my own research and found no article saying anything about taking a rocket to the Moon on a suborbital flight. I am hoping that possibly I might find the answer here.
A "suborbital" trajectory to the moon could be done--simply never raise your periapsis above 0. However, there's no reason to. By the time you're at the moon the difference between a periapsis on the surface vs a periapsis in low orbit comes down to 5 m/s.
To save that 5 m/s you have to accept an instantaneous launch window (no waiting around in orbit to get in the right spot) and you'll probably waste more in not having as accurate measurement of your position.
I rather suspect what you saved in KSP is even less and I'm sure you used more trying to do a manual burn than if you had used MechJeb to control the burn. (MechJeb has finer control than the keyboard.)
The reason that NASA does not fly on suborbital flights to the moon is because of one major factor. If you somehow got the needed delta V within a second then the delta V needed would be less. The issue is the Hohmann effect. Since the rocket is flying straight up from the earth the effect from the delta V is getting smaller. At a certain point you would need more delta V to fly on a suborbital flight to the moon. Since NASA rockets like the SLS or the Saturn V do not accelerate fast enough, it would not make sense to fly on a suborbital trajectory. If you had a model rocket that could produce the delta V needed and maintane around 5G acceleration then it would be more fuel efficent to fly on a suborbital flight to the moon.