When BTT works, then "starting: it from Application folder or from Spotlight window should bring configuration window. This can be an easy way to go to configuration for people more keyboard-oriented. It was working this way in the past but after UI change stopped. I think that it is oversight, as many Menubar apps works the way I request.
I think the behavior hasn’t changed:
If BTT is running, starting it again from Spotlight or Applications (or any other way) will open the UI. If it’s started while it is not running it will stay in background.
I don’t think there is a way to determine how the app was launched.
There is a flag you could set every time BTT is started, that flag causes the UI to show up after the next start. I need to lookup the name though (currently not at home)
You could also configure a shortcut in BTT and assign the „open BetterTouchTool preferences“ action