I’ve never done this before, but what I would try is this. In your audio editing program set up a track with the audio in it (Track 1) and mute it. Then set up a pre fade aux send in Track 1 and return track (Return 1). On Return 1, insert a reverb (big hall). Set the parameters so that all you hear is the completely “wet” signal on this track. This will be your “pre-echo” as you call it. Now go back to Track 1, set up a second pre-fade send and return track (Return 2). On Return 2, insert a delay unit and set it’s parameters to a completely “wet” signal (you want to hear the delay only). Set the delay time at 500ms to start with. You’re trying to get this signal to be the main audio that you hear after the pre-echo. It sounds like this track (Return 2) will also get a touch of reverb to taste. Then it’s just a matter of massaging and tweaking the audio to get what you want.
May not be the “right” way (like I said, I’ve never tried it before), but it certainly is one way.