The main problem would be getting the necessary atoms to your factory. It likely would be easier to construct fuel on earth or on the moon and send it up. (If your rocket exploded the ‘BOOM’ might be a bit louder if its cargo were rocket fuel instead of raw materials for rocket fuel, but the practical difference would be zero)

Your best bet would be to use mass that’s present in space, but unfortunately (1), there isn’t that much in orbit. In theory, one could scope up cosmic dust, tiny meteorites, and old satellites in orbit. It would be a challenge to scale that up, though. https://en.wikipedia.org/wiki/Stardust_(spacecraft) didn’t catch kilograms of stuff, even though it explicitly went for a comet.

Capturing a larger meteorite would work, but larger meteorites are harder to catch.

If you’re extremely ambitious, build a solar powered particle accelerator in space, use it to create electrons, neutrons and protons (https://en.m.wikipedia.org/wiki/Matter_creation), turn those into atoms, and build fuel from those (apart from the practical problem of scaling that up, there are ‘a few’ Ph.D’s to be earned there.)

(1) or fortunately, as having lots of mass there would make space flight dangerous (https://en.wikipedia.org/wiki/Space_debris)