Drinking can be a big part of socializing in the US, but you'll be able to get by without it. Neighbors don't come over uninvited here, and it's unusual to have the type of friendships where people come by unannounced all the time (at least, after college).
I might try a few things:
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If you haven't already, find a local mosque to attend; that's a good way to widen your social circle with American Muslims, who may be able to introduce you to more people, broaden it further, etc. It'll be folks who are more culturally familiar, but many will likely be a bit more integrated already and have a wider group of American friends as well.
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Hobby based clubs are great, but they do tend to be a little transactional -- think about hobbies you want to be doing anyway (so you're not JUST there to meet people).
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If you have the time, I'd be on the lookout for volunteering and community service type activities -- it's a great way to meet good people, more committed than a hobby group, and much less awkward to socialize in than a workplace.
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Depending where you live, try and strike up conversations a bit more openly / frequently, and be willing to mention that you just moved here and don't know many folks. At the barbershop, out to breakfast, in a long line, at the coffee shop, etc. Make conversation, a lot of people will be happy to chat and some will invite you to things. Just gotta be ok with lots of chats.
ADHD and depression are super, super comorbid though.