Can I make the donut cake without the filling the day before serving and fill the next day right before serving?

Pending reply from Sarah Jampel, I think you'd be fine.
If the cake had been a real giant fried doughnut, no. (that should be eaten same day, best soon after frying)
But it's actually sweet yeast bread (brioche) and can keep for up to 3 days in a tightly covered tin.
Yes, add the filling just before serving.
Sounds both pretty and delicious.