In my opinion, universal brotherhood cannot be propagated among the existing population but can be done with the successive generations of people by imbibing certain qualities within them.
For centuries, humans have been at war with each other and even today the tradition continues, albeit at a much smaller scale. This means that we are actually moving in the right direction, but, at a snail's pace. All of us individually wants universal brotherhood but collectively it never seems to materialize. The reason is that we have to consciously make an attempt to attain it and therein lies room for failure.
But what if we had no choice? What if all we knew was to live peacefully? If every child born did not know the meaning of war, only then the world would be at peace, this is nothing but a pipe dream because children watch and learn. This means that their parents' generation must also be at this level of… restraint for the lack of a better word. Going by this, there can never be a ‘first generation' of people who have achieved universal brotherhood simply because it's not possible unless we isolated them from the world and had an automated system of allowing babies to grow up under a controlled environment (What a terrible idea and a great one for the next apocalypse-themed movie!). It's a paradox, really. There is also the question of war being one of our basic instincts, it is not feasible or healthy for the whole world to be at the same level of wealth, power, happiness, etc. and there has to be disparity among the people, it would create a havoc any other way and we would end up being a bunch of zombies instead of humans and with disparity comes competition, ambition and ultimately war. So, instead of achieving universal brotherhood, we should look at universal humanity which may be a tad more feasible.
All this explains why moving at the current snail's pace is actually the best bet for us to achieve what we seek, it is an extremely slow process but nature always acts in the long term and our life is but too short and our field of vision too narrow for us to observe these changes.