My two cents. As a social anthropologist (ahem) I would say that “mainstream” creativity is driven mainly by socio-cultural factors, not so much by genetics and biology.
This means that individuals’ creativity is determined by the social and historic context in which they grow up (family, society at large, traditions, culture).
There’s quite a lot of cross-cultural research on factors that play a role in creativity, such as individualism, sociality, socially induced forms of perception and representation. Historical evidence (comparisons of creativity in Catholic-Latin cultures versus Protestant cultures for example) points in the same direction. Latin cultures have a very “sensual” view on life, which is the result of Catholicism’s materialism. This has led to highly creative cultures; Protestant and Calvinist views on life are anti-sensual and extremely cerebral, which doesn’t really stimulate artistic creativity (not many works of art come from Finland or from white Protestant Americans). It’s the difference between Brazilian samba musicians and Scandinavian architects. 
But then it all depends on how you define “creativity” in the first place.
Back to the role of the social sphere. If you were to be able to change a culture and its social mechanisms, you could probably enhance people’s creative skills. But this is only so for “groups” of people, not for individuals per se. There’s always the factor of “talent” that is probably genetically determined. Changing the social and cultural sphere in such a way that this talent can surface more easily, is probably possible.
On the other hand, there is some science suggesting that true geniality may be related to pathologies such as schizophrenia. This is genetics.
Then again, some cultures make a place for schizo-paranoid individuals and allow them to take on certain roles (artists, musicians, religious leaders, etc…). Other cultures put them in asylums or reduce them to autists. So here too social structures play a role.
In conclusion: I believe you can stimulate ordinary people’s creativity by intervening in their social environment (e.g. a non-authoritarian education, a family and peer environment in which artistic expression is encouraged, etc…). This could boost “mainstream” creativity. But genius and truly exceptional creativity are probably determined by genetics and cannot be taught.
Something like that, dude.