When loading our game in WebGL, there is a time after the HTML loading screen goes away and before the Unity splash screen where a black screen is displayed. Is there any way to go about removing this or reducing the time this is displayed?
Did you try alternative HTML templates? See Player Settings.
This issue happens with all of the templates from what I can tell.
You can solve this with the template as suggested by @CodeSmile - As an example have a look at this template.
What I’m doing there is fading the loading screen out in these lines. You could do something similar or add a delay before the loading screen disappears.