In alexa custom skill, it is possible send an intermediate response before sending the final response. For example, we can send "Please wait, I am looking for the rental car .." if it takes time to search for the rental car. Is it possible to send such "Please wait.." message in Google home custom action before sending the actual response?
No.
The best you can do is to send a response and include a Media object with it (sorta like "hold music"). When the music is done, your Action will get a MEDIA_STATUS Intent.
Your search needs to run in the background and save its results in a cache of some sort. When you get the MEDIA_STATUS, check the cache to see if results are available. If so, send the results, otherwise, repeat.