As mentioned, keep practicing. Get into an empty lot and practice repeated starts. It'll come.
Don't worry about hurting the bike; you won't.
And don't worry when you do stall on the street; keep calm, re-start the bike and carry on (Chive pun there).
I went to take off from a stop last week and didn't realize I'd left it in 2nd. I stalled. I've been riding since 1988. It happens.
+1
Practice your emergency braking while you're at it