I use MS-Office 2016 and MS-Office 2008 equally on my 2006 Mac Pro with El Capitan 10.11.6.
I've never had that problem. I'd expect that something is causing a delay between when you press a key, and the computer realizing that you intend to enter information.
One thing does come to mind, since you indicate that it occurs after a period of idle time. Perhaps the first keystroke is "waking" the computer from some type of idle power saving state?
For example, if my computer has been unused for a few minutes, I have it set to go to the screen saver and require a password to unlock it.
When I press a key, it brings up my password box. But the first keystroke that I used to exit the screen saver does not show up in my password box. Only the 2nd keystroke and later are applied to the password box.
So... I'm thinking that if you haven't typed for a while, that perhaps your first keystroke is a "wake up" indicator, and then your second keystroke is entering information.