What do you mean by conflict???
What do you mean by advance?
If by conflict you mean war, or violence, then I say no!
If you mean disagreement, lack of unity, then I say yes.
If there is freedom (and we must have freedom), then diversity must expand, and with diversity comes conflict in a sense. But if we are sufficiently advanced, then such conflict need not result in violence of any sort. Reasonable people can and must agree to differ from time to time.
To me, advancement means accepting that many of the simple ideas from our past are no longer useful. Simple binary notions like true/false, right/wrong etc, when applied to reality, need to do so with probability statements attached to them.
Uncertainty is a fundamental aspect of reality. We all need to accept that.
So to me, advancement means both accepting eternal uncertainty, and accepting expanding diversity.
Much of our current educational and social systems seem to be designed to constrain people within sets of ideas. Much of that is no longer appropriate.
Certainly, everyone must accept limits on freedom, all form demand boundaries in a very real sense. And the limits actually required to sustain humanity are far less than most of the laws currently in existence; most of the cultural limits currently in existence.
So there seems to be considerable space to modify the notion of legal limits, and to reduce the number of laws that apply in most contexts; at the same time as we must acknowledge the need for some limits on freedom, simply to allow our species to survive (and that can actually get extremely complex in some contexts – and can be quite simple in many contexts).
So plenty of room for advancement (in terms of: individual security, individual liberty, social responsibility, ecological responsibility, acceptance of diversity, support for creativity, etc).