Rome was originally a city state comparable in size and development to many other sorrounding ones, including many Gaellic ones. It grew and developped in the same way as all those, through haphazard alliances and trade routes, etc. Rome at one point reached a critical mass of advantage beyond which it transcended into a different level of power than the others, an imperceptible point but quite irrevocable, that only became cristal clear once the truly old, established and civilized Carthagenians were defeated. The Carthageneans, by the way, whose plan of attack was to ingrain themselves in the haphazard networks of alliances Rome was part of on the side of her enemies, so that the war against Carthage was also largely a war of Rome and her allied or client city states against the opposed networks of neighbouring city states, or tribes.
It wasn’t a spaceship with aliens that landed and started subjugating the poor Europeans with their poor cultural traditions.