The fastest and best way to build a creative culture is to have lots of creative people together. No kidding. It works. Hire creative people, they will create a creative environment (because the leaders will be creative) and we all will be creativists.
I am not pulling your leg. The issue is that we often hire lots of non-creative people, people who have never created anything (seriously, never, not even in school) and then we say: we want an innovative culture, we want you to be creative. It does not work.
Problem two (the above was problem one) is the inverse. We hire or gather lots of creative people, but we ask them to recite the yellow pages in search of the Big Idea. Bad idea.
Back to the creativists. Many people can innovate and be creative if, and there is an if, the environment pushes them that way. Innovation is going to the mental gym every day. No gym, expect arthritis.
Creativity is very sensitive to suppression. It’s actually quite easy to curtail. The education system in many places is a benign straitjacket. Entering the school system as a question mark, leaving as a period , a la Neil Postman.
Leaders have to create the conditions for creativity and innovation. I don’t buy the functional and professional boxing: accountants are not creative, engineers neither, and designers (particularly the ones in a garage) are full of uncontrollable creativity (And don’t try to put the accountants in the garage, you will waste your time and it annoys the accountants). I have met incredibly creative engineers ( and accountants) and lots of emperors-with-no-clothes designing in garages.
Bottom line. Expect miracles if you wish, but to accelerate that thing called creativity and innovation, (1) transplant those people and give them the space; (2) add not-so-innovative people; they will copy the others.
Even in the case of creativity and innovation, Homo Imitans  works.