Also note that modern radars are sensitive to how fast an object approaches (or leaves) the radar. Bumblebees don’t break the soundbarrier usually, so it is possible to see these planes, but you do have to tweak your radar for it. (Hence why the US doesn’t give specs.)
You are talking about Doppler processing. Basically you can filter out all the things that are not moving fast based on how much the frequency is compressed and lower your noise floor. You will still have other noise sources but minimizing clutter will help, if the return is below other noise sources you still will not be able to detect it.