I have been poking around wondering about the colloquial usage of on tomorrow in southern american english and wondering about. You can say, do you work on tuesdays? Tomorrow morning is idiomatic english, tomorrow's morning isn't.
Starting 5, June 4 Game 1 of the 2025 NBA Finals tips off tomorrow
So your sentence we start tomorrow is proper in this context.if meant to be a question a question mark should be added, we start.