Well, half a book on that topic, and more extensive writings on Space Systems Engineering. I'm working on updating both.
Both of you mentioned self-replication as a method of expansion. I talk about self-expansion using three methods:
replication, or making exact copies of parts and machines, which has a fairly extensive literature,
scaling, or making different sized parts and machines than you started with, and
diversification, making new parts and machines not in the original set, although the plans for the new machines may be present from the start.
I see combining these methods as both easier and more powerful than self-replication. Replication requires making 100% of your own parts. A starter kit with a small number of machines (~6-8) can make some of it's own parts, and parts for new machines. The remainder are imported from elsewhere. As it adds new machines to the collection, it can increase the self-production percentage, eventually approaching self-replication. New parts and machines includes making better versions of the same machines. For example using a lathe to make a better lathe.
I know a self-upgrading starter kit is possible, because that is how tool makers have always worked. Starting with animal skins, rocks, wood, and iron ore, you can make a bellows, furnace, and charcoal, and then smelt iron. The raw iron flows into two molds at the bottom of the furnace, to make a large lump and a smaller lump or two. The big lump is a crude anvil, and the small lumps make hammer heads. With a hammer and anvil you can now proceed to bootstrap the rest of your metal tools, and you are off to the industrial revolution.
A starter kit is a feasible design problem, and it doesn't have to be perfect the first time. Over time people can improve and optimize the growth path and reach near-replication faster. I say near-replication because a typical location on Earth or in space won't have the ideal mix of raw materials. So some will need to be imported from elsewhere. Also, some items will be too complicated to make relative to the number you need. Computer chips are an example. You might need a few dozen in your starter kit, and that is not worth setting a chip fab for. It makes sense to import such parts, at least in the early growth stages.
So I assume a "mature" factory that grew from a starter kit will be around 98% self-producing, and import 2% rare materials or complicated items.