The development of something so complex as a nuclear bomb, or for that matter many of the world's modern experiments such as the Particle Physics Labs; and the amount of open access needed to investigate biology in exotic and perhaps dangerous locations; and all sorts of other problems that don't occur to me at the moment, together probably mean that the world has to be (relatively) civilised before science can really take off. A great deal of the progress made in the 16th-19th centuries was essentially in smallish groups, but at some point this becomes no longer enough and you need time, money and lots of people involved to take things to the next stage.
So anyway, civilisation would need to have happened first in any case. As to how much further forward we'd be if the world had settled down enough to give us the opportunity -- well, presumably at least a few centuries more advanced. Among the things I'd expect us to understand in the next few centuries would be:
- how to do practical quantum computing
- better disease control
- An understanding of fundamental physics up to at least 1000 times higher energy than we are at today
But presumably either of two things would be added to this: not only would we have probably "finished" current directions of research but new ones would have been thought of, finished and prompted other new directions, and so on and on; or alternatively the world would be such a different place that some very different directions would have been taken from the start. How productive these would have been is anyone's guess. I'm always slightly sceptical of the values of such speculations because so much of what we've come up with was driven not just by idle curiosity but also by the circumstances of the world at the time. Better timekeeping technology, for example, owes much to the dangers of navigation at sea, which in turn was mainly a problem because of the European bent for sailing off to the New World and conquering or exploiting its resources -- if we'd stayed at home instead, in a peaceful world, would this have been such an urgent or important project?
Although Science certainly isn't a linear progression entirely (there are lots of dead ends and the occasional resurrection of old ideas that take you away from a single line) it is usually true that the next generation of work builds on what came before it, and at some point you find a starting point of a particular problem needing to be solved for whatever reason. A World with different problems would need different solutions, which would surely lead to a wildly different set of ideas and lines of thought to be followed. Perhaps, in the end, because the Universe would be the same place we'd have still made the same discoveries -- certain things are always going to be true -- but we would at least have got there in a very different manner. There is even a chance that we might even be behind where we are now. Well, why not?