As far as I know, when you play an audio file, unreal engine has to load the entire file before playing it, it doesn’t load it in the sound cue directly when the sound cue starts (only right before the actual audio file starts). That’s why you have this delay; that particular sound file is loading. Therefore, the only solution is to load both of the files at the same time, and play the looping sound exactly when you need it.
I found this post that should hopefully be helpful: