In C++ suppose you have an unordered set (https://en.cppreference.com/w/cpp/container/unordered_set) of strings - is there a way to efficiently extract all strings from that set that meet a certain criteria (e.g. find all strings in the set that begin with letter "a") using a method other than iterating through the entire set with a for loop and checking the first character of every single string?
For any criteria this is not possible, see this answer for some more details.
Depending on your other needs, a sorted std::vector is highly likely to be the most efficient for the extraction part alone. Use algorithms like std::lower_bound to work with a sorted std::vector. In the end, your actual use cases is what determines overall which container is best suited performance-wise - although std::vector comes close to a one-size fit all for considering performance (this is because of all the internal optimizations of contiguous storage).
That being said, in general it's advisable to use the container that seems best suited for the problem at hand and only do clever optimizations if there's an actual performance bottleneck.