Can I get viruses without downloading anything?

I clicked a link and it redirected me to a website saying that my computer had a virus. I have not noticed any problems it just kind of scared me. It did not download anything and I know that is the only way a mac can get viruses.

So, is it possible for it to download a virus without asking me to confirm or without even showing anything being downloaded?

Would really appreciate some help because I really don't want any of my information being taken!