Our document has a very high waiting time and very low receiving time.
Is there a way to get the document to start receiving earlier?
The waiting time is basically the time it takes your server to understand what it should do. When you send a request to a server, it will take time from the initial contact to when it sends its response (waiting). So the only way to speed up the waiting time is to speed up your server. Now that can be done with more then just a server upgrade though.
So here are some questions to ask yourself to help troubleshoot.
How many extensions do you have? Do some pages take longer then others? If so what exact extensions load on those pages or are there alternatives? Is Joomla up to date? Can you test an upgrade and see if that helps (with backup ready)? Can you live with out them? Is the server taking a high load?
But in all honesty for 14ish kb of data and 500ms to load it, its not lightning fast but in my opinion nothing to really worry about to much either. Although the image does not show the actual waiting time, this page totaled 320 ms with 12kb and this is stackoverflow! Not a huge difference.
Optimizing your database and making sure your extensions are efficient is the best way to lower it without going into your actual server settings.
As Jordan said, improving your server speed is likely the best way to go here.
There are quite a number of optimizations you can do to improve your waiting time. Here are some of the server side optimizations.
NOTE: As far as I am aware, Redis cannot be used with Joomla versions < 3.4.
On the Joomla side of things you can
There is a slight chance that the page load time might be having an adverse effect on your waiting time, so
Shared hosting package? Move your site to a better one.
Shared hosts must allocate server resources to the request of all sites on the server, the more accounts on the server, the longer the response time of each site. You can cache an optimise, and you should, but when there's 200 other user accounts all with multiple sites on the same physical server as yours that isn't going to make the world of difference. A better specced host will make a huge difference.