"Rome wasn't built in a day", goes the popular saying, and it hasn't ever been truer.
Civilisations are formed from the co-operation of thousands upon tens-of-thousands of individuals, each possessing relevant skills and knowledge enough to survive and prosper by converging together - generally under the leadership of a select capable sect - in the name of life.
The people of the largest or strongest civilisations, in almost all cases, originated form the same planetary origins - regions, countries or pre-existing colonies that expanded their numbers by conforming the populous of surrounding locations to their way of life. Their pre-existing social cohesion acts as a foundation for further empirical growth, which without would see any hope of a greater civilisation fall to pieces (there being no trust or structure or purpose among it's members).
Simply dropping a million persons, from all regions of the world, with very little in common in the way of cultural likeness, language and beliefs, is a recipe for civil destruction rather than growth. By simply looking at humanities judgments toward each other, to those ethnicities other than oneself or social minorities today, it becomes apparent that this will be no leisurely journey...
Dunbars Number refers to the theoretical limit to how many relationships a person can maintain at any given time, derived from the regular brains capacity for storing information; every single relationship made will count on this planet. 121
These million people (or those who survive the initial splash down) will form instant connections with those they relate to on a more personal/cultural level, immediately dividing the future-civilisation, for despite them all being in the same survival situation, pre-existing bias/barriers still exist; this will need to be over-come if there is to be any chance at colonial development.
The skill range of these people will also need to be taken into account; by law of distribution, almost no-body in the million will possess the skills relevant to survival (accounting or quantum-physics not exactly the most helpful...), potentially thousands having no knowledge on life at all (being children or un-educated) and those who do will be limited in who they associate with to begin with...
This civilisations best hope comes in the emergence of a clear governing body, a caucus of people who share the essential knowledge of survival - hunting, farming, construction, human resource management, health care- who will be most qualified to lead the masses; but as explained, this will be no easy task and could potential prove to divide the emerging culture more.
So.
This established, how long will it take?
In a word entirely devoid of usable power, functioning technology, advanced tools and appliances, basic shelters, readily attainable food sources... Civilisation is going to take a while to take off.
If a leadership group emerges, it will most likely only get a small fraction of the million to co-operate, humans being largely self obsessive, the rest resisting to form their won splinter "alliances" with those people who most resemble one another in ethnicity, language, culture or belief system. This isn't such a bad thing though, provided violence remains frowned upon and any who commit "felonies" are dealt with according to judgement of the majority (hence the beginning of a justice system).
The groups would live in relative proximity to one another, forming ever more intricate housing over time, as people learn from their leaders or from experiencing failure (the gathering and distribution of essential knowledge); any non-vital information will be forgotten over time (as those who held it die/ find it irrelevant).
As groups form alliances with their closer neighbours, they may merge, this process continuing over the course of generations until there remains only one sole community of which internal social sects (the original groups) provide a different skill set or value to the civilisation as a whole - just as modern day people live and work. 998