I had this in my past job. Have 1 QA per two developers, the QA sits with those two developers, and you are constantly telling them when a build is done and on staging. They write tests, do some manual checks, and then tell you how it is going relatively immediately. They also handle the problem of reproducing bugs and narrowing down exactly where they occur, which is not trivial.
For all the faults in that organization (including letting our test runner be broken for months), we didn’t put out a lot of bugs and we found all manner of strange edge cases very quickly.