Don’t we have engineers who could take one apart and reverse engineer it?
Add a bell or whistle — and patent the “improved” design.
It's very, very hard. The problem is not in the drawings - they can be trivially recreated with modern 3D scanners. Would take just one day, probably.
The real devil is in the details that are called "material science." It is not enough to mill a part from a nearest piece of steel that you happen to find under your workbench. You must use the exactly right brand of steel - which may, not very unsurprisingly, be made only in one place on this planet - in a little town near Moscow. Can you recreate this steel, since you have every scientific method available to analyze a sample? Well, maybe. Or maybe not. Metal alloys are not just chemical compounds - they are a collection of crystals, and these form in unique conditions of a specific furnace. Sure, you can always go with "close enough" - but these parts work in pretty demanding conditions, and if they fail your entire vehicle will be spectacularly lost.
Should the USA start the work? I'd think this would be a far better application of tax money than helping ISIS in Syria and simultaneously blowing them up in Iraq. At very least it's possible to make something that is better than the RD-180 design. But this work will cost a lot of money and will need a few years of trying, testing and failing - and going back to the drawing board until it's perfect. You cannot make a replica in a few months; doing it in one year would be, IMO, very doubtful. Two years - perhaps. But the political demands are "right now" - and there is nothing right now.