Q: build the culture of something/ culture building In my native language when we want to mean educating people to do/think the right thing and persuading them to do so in different ways such as advertising, punishment, encouragement, rewards, shaming etc., mostly done in a broad scale, we say things like these

It's necessary to build the culture of wearing seat belts.
We should wean people off plastic bags and make them use cloth bags instead. I know we can't really force people into this, but we could atleast start its culture building in our media!
The necessary culture building must be done first before letting the immigrants into the country. People could be really unkind to them because they'd think they came here to take their jobs away.

Interestingly, I can get results for culture building, but it seems there's a difference between what I think it should mean and what's there to mean. Do the sentences above read natural to you? If not, is there such a word/phrase to mean that in English? How do you rephrase my sentences?

A: According to this google ngram chart the form "building a culture of" is moderately frequent, but almost unheard of before about 1985, but "building the culture of" is very rare indeed. According to this related chart the form 
"build a culture" goes back farther, but "build the culture" is not and never has ben anything but rare.  
Your example sentences are understandable, but there are certainly not something i would write myself, and "culture building", like "nation building", to me suggests something some from the outside, or something done by an SF author creating a fictional culture. 
I agree with the comment by Tᴚoɯɐuo that "create a culture" or "foster a culture" are more natural expressions in English.
