However universities and research seem to have something against common convenience and most of their offers are hard/impossible to find/search.
Do you have any resource where I can find PhD opening that offer VISA sponsorship?
The difficult part is identifying professors that you'd like to work with.
My emails were clear, simple and respectful. I guess they have better things to do than to respond to random stranger on the internet.
I wish there was a kind of a job board for PhDs ..
https://www.google.com/search?q=phd+position+site%3Ahttps%3A...
Some PhD openings may not even be advertised, so politely asking (i.e. no generic spamming) existing students or faculty members is the only way to find out.