Sure. If you have the input materials. If you're at the point of having to build an alternator by hand rather than just taking one off a car, I'd like to know where you're getting magnet wire, the machined shaft, the various rotor and stator parts, the end-bells, and the ball bearings.
Consider that you're not necessarily building from raw materials, you will be repurposing things you find around. Finding an alternator probably won't be a problem in the populated areas of USA but might be elsewhere - thankfully building it is still sufficiently simple.