Typically you both say a greeting then a conversation starts.
> Instead of being polite, you are just making the other person wait for you to phrase your question, which is lost productivity.
Please don't count every second of your life in productivity lost to someone else.
The root of the problem might be frustration with not getting something done, and that needs your reflection.
Or just wake up 3 seconds earlier, and if worried about lost sleep, get to sleep 3 seconds earlier or in the words of Arnold Schwarzenegger "sleep faster."