acoustic signal when game starts in another tab too late

Hello,
everytime a game starts in another tab it is displayed in the header of the tab. Nevertheless the acoustic signal (a kind of bling) is played only if I already changed to that tab. Is it possible to set it the way I get informed already BEFORE I change to that tab? That would be very helpful.
Sincerely,

Update: it would also be helpful if anyone could respond so I know I'm not the only one with that problem? :)

When a game starts I normally get the acoustic signal *after* I made my first move.
But I get a device notification when a game starts while I'm on another tab.