No, these engineers at FAANG companies could not solve those problems cold without having been taught how. I have worked at two, which is how I know. I have never seen a question in an interview I haven’t seen before. Many of these questions went unsolved for decades in the industry, so no, these engineers, who mostly aren’t DSA experts but distributed computing experts, could not solve them cold. I also saw how interviewers used questions to re-enforce their own biases on university, gender, or home country in these interviews.