Would it be possible to begin mining asteroids and create a space-based manufacturing infrastructure using...?

It's impolite to keep repeating your question.

CAD/CAM and 3D printing offers to bring the ability to manufacture more products with a smaller infrastructure but getting started in developing space is a matter of boot strapping the infrastructure itself. You have to build the first colony in space which could then be a base for future infrastructure. Because of the costs of launching from Earth, it would have to be of in-situ materials which amounts to regolith from asteroids, CO2 and water ammonia ice from comets and some asteroids. Because of the cosmic rays and solar winds, you can not have a workforce till shielding is available as in at least the exterior of a habitat. Hence it has to be by robots and be as simple a manufactured product as possible which can still provide the shielding for a workforce.

I believe it shouldn't be anything complicated like CAD/CAM or 3d printing at least not initially, it should be just mining, smelting and drawing wires. Wires are already spun by machines into cables. Cables can be knitted into structures, we already have machines that knit clothes from yarn and even weave screens from wires. The knitted structures can be filled with slag and regolith to form a radiation shield enclosure. Knitted structures can be thermite welded solid to form air tight structures and generally, a habitat can just be such a crude structure. Once you have a colony in habitats, you can have whatever manned manufacturing that you'd like ( vacuum vapor deposition 3D printing is very promising ).