Assuming a humanoid robot with human like intelligence it may also be able to enlist humans to accomplish it's task, either by paying them directly, or through intermediaries, or deceiving them into helping it.

If it is capable to human like intelligence and creativity it may be able to pioneer new manufacturing processes -- perhaps it will learn to grow parts for itself by using existing biological processes in ways that we haven't yet figured out.

The point isn't so much the how with a self replicator, the point is the exponential growth rate. You're right that the first machine will take a long time to build the second, but those two will certainly be able to build twice as many in at least the same amount of time -- probably less because they can use the infrastructure that the first set up to build the second.

Once humans make machines that are capable of self replication regardless of where it is on the spectrum from base matter and energy assembly to just off the shelf parts assembly you're going to see exponential growth.

And once certain kinds of creative people get their hands on these machines they will inevitably jailbreak them and make them work for them instead of the companies that will try and lock this kind of stuff down like they always try to do.

The war on general purpose computing will transition into a war on general purpose manufacturing and the same kind of people who want ot sell you devices that you can't compile software for without a license will try to do the same with self replicating hardware but they will fail.