NEEDING to buy 3 cores to Start L5R was a hard pill to swallow.

Assuming I'd buy a few deluxe & pack expansions in an initial purchase, do I need to buy >1 core Netrunner boxes, or can I stick to one?

I've seen a few resources on how/what to get started, but none specifically clarified the number of core(s) needed at ground zero.

One core is just fine.

Also, you did not "NEED" three cores to start L5R - I did just fine with one.

It is my understanding that you only need multiple Core boxes if you want to play competitively. Even then, you should be fine with two.