There’s a wonderful organization that helps place Jewish children in Jewish homes. It’s the Jewish Children’s Adoption Network, run by Steve and Vicki Krauss of Denver. It’s true that it’s quite rare for healthy Jewish infants to be available for adoption, but there are children who are older or have health issues. When we were looking to adopt, we (of course) asked a posek whether we should seek to adopt Jewish children, and we were told that we should.
It’s probably extremely rare for healthy children of frum parents to be adopted by non-family members, but I have heard of one case. In the past, in some segments of the frum community, children with disabilities may have been given up for adoption, but I think that’s less prevalent now.