I would say that there is not much of a “culture” around green tea specifically, as there tends to be a much stronger culture of black tea, at least where I am on the east coast (Hot black tea in the Northeast/New England, iced/sweetened black tea in the Southeast).
As others have stated, most Americans would be familiar with it in teabags or bottled green tea, and so many who do end up trying it don’t enjoy it because they end up trying a bitter, lesser-quality version of it. Others may be familiar with it in Japanese or Chinese restaurants, where the quality is hopefully better, but this probably cannot be rightly called American green tea culture.
In my experience, it is the sort of thing where the green teabags might be the only ones left in an office meeting room because, while someone thought to stock the meeting room with green tea in the first place, all the others have been used up first and then someone has forgotten to refill them.
It largely depends on whom you’re asking. I think your average Midwest American doesn’t know what it is. Or if they do, don’t really care for it or like it. Lipton bagged black teas are their standard. Usually served with a lot of sugar and or lemon juice.
Arizona Tea company has a sweetened green tea that has been sold in major grocers and convenience stores for decades. It’s very popular and is known for it’s cherry blossom motif. I don’t want to rag on them because I think they’re a decent company, but it’s sugar water and green tea might be loosely defined there.
Boba culture has made the younger generations aware of green tea. And they can give you a run for your money when it comes to cultural knowledge. But they would be largely clustered in urban and suburban neighborhoods.
In America, when I see a non-Asian person drinking a boba tea or even a Starbucks Matcha it warms my heart just a little.