None of my friends are friends with me 'because I help feed people with AIDS every week'. Probably most of them don't know that I do this, and maybe this is pretentious but I don't make it public knowledge because in the past when I have it has intimidated people, possibly because they get worried that I would get judgey.
I would go so far as to say, even better than doing something good and 'caring' for someone (you should do that anyways) is to get in debt to someone. Maybe not financial debt, but ask other people for a favor, or help. Psychologically, the person is then invested in you to repay that debt in the future. After all Kennedy said "ask not what your country can do for you, ask what you can do for your country", thus putting the country in debt to its citizens, and his popularity soared.
I think you misunderstood the "help other people" with "do volunteer work". The two things are not necessarily related. Nobody is going to befriend you just because you help children with troubled families, but surely they will be more likely to befriend you if you help them with their everyday life, like helping them moving out of an apartment, giving them a shoulder to cry on when time is rough, buying them a beer after a bad night, helping them fix their bike, etc etc.
It's not about helping everyone, it's about helping the people you care about (supposedly, your friends)
This is about you helping strangers, or friends of friends. Moving, cooking dinner, helping with a legal problem, helping them with their exams, letting them borrow your rice cooker over the weekend, helping them with their birthday party, inviting them for a drink, volunteering to look after their dog and so on.
I think that's tricky. If you help people too much, then they resent you because of the built up debt (which is why I wrote the part about debt in there). It's counterintuitive, but I think asking for help is a better strategy for making friends than offering help.
I would go so far as to say, even better than doing something good and 'caring' for someone (you should do that anyways) is to get in debt to someone. Maybe not financial debt, but ask other people for a favor, or help. Psychologically, the person is then invested in you to repay that debt in the future. After all Kennedy said "ask not what your country can do for you, ask what you can do for your country", thus putting the country in debt to its citizens, and his popularity soared.