Just because you’re a rocket scientist doesn’t mean that you have all of the disciplines under your belt needed to launch a craft. There’s a lot of comptuer processing and modelling and stuff you need to have that would be difficult to accomplish alone.
You’d need several tons of very particular materials for fuel, which would most likely cost a good fortune, if even accessible to private citizens in large enough quantities.
You’d need machinery that allowed you to build things to very particular tolerances. Just because you have access to the parts doesn’t mean that you have the capability of putting it together well enough. And anything you tried to fashion yourself would most likely be unsuitable, again, unless you had the ability to meet strict tolerances. Most likely you’d be restricted to building something that was essentially already built and designed and was simply in parts.
Overall, it would be mostly infeasible to construct anything larger than maybe 10 feet long–which would probably already be inordinately heavy–and I’m not sure whether that’s got the fuel mass to break out of orbit.
Earthly rocket, yes certainly you could build one. Apollo? No…I’d be highly doubtful.