The problem is not getting a rocket to space, it's getting a human into orbit. If you just want to put a rocket into space what you need to do is:
1. Get some weather balloons to lift your rocket to the edge of space. This is actually pretty easy. I read an article about some college students who did the same thing to take photos of space. Minus the rocket.
2. Drop your rocket payload.
3. Ignite the rocket.
4. Let it fly until it is technically in space. About 100km up.
5. let it fall back to earth.
6. Gloat
You can add a shoot and a GPS tracker if you want the rocket add weather balloons back in one piece. Because the rocket is not going at orbital speeds there is no need for a heat shield.