I'm going to go devil's advocate here and say I think it very much depends on how capital-focused your early empire is, and that I'm not convinced that the NC - and early-game tech in general - are anywhere near as big a deal as they're often made out to be (at least on immortal and below).
I think you can really cripple yourself by chasing science too hard too early, instead of investing in overall empire development. Tech in itself primarily provides you with opportunities, rather than concrete and immediate benefits. You have to have the development to actually capitalise on that tech - there's not much point racing to Education if it then takes you forever to actually get those universities built, and if staffing them then cripples your cities' future development. Or if racing to NC/Education means that someone else has taken all the good land because you didn't expand.
I've been playing wide lately and finding that I get much better overall results the more relaxed I am about science. With a wide game in particular, you don't really need much in the way of tech early-game - a steady stream of settlers, workers and archers, couple of trade units and then a few monuments, circuses and colosseums as appropriate. Libraries are way down the list of priorities. I've found myself sprawling out to about 7-8 cities while filling out the basic worker techs and construction, then going for writing as pretty much the last ancient era tech, then hitting philosophy about when the empire is ready to build the NC.
Yeah, you end up a long way behind in tech this way, but you're not gonna run out of stuff to build. And a few extra troop numbers will do fine in holding off an attack from a technologically-superior enemy. You get a fair bit of tech from trade routes and settling a scientist at the end of Liberty, and it gives a nice production/population base that can really accelerate your tech for the rest of the game. Tech parity by late renaissance/early industrial on immortal, in my experience (with unis in only about half my cities - probably faster if you really focus on building libraries and unis everywhere).
I'm sure plenty of people will disagree with this approach (and you definitely want to focus harder on the NC if you go tall), but below deity you'll be amazed by just how easy it is to catch up from a tech deficit if it was incurred in the good cause of developing your empire.