It's very evident by the amount of damage to the front of the offenders car (& the back of your car) vs the very tiny amount of damage to the front of your car (where you were forced into the car in front) that you were pushed there from a high speed rear end collision that the other person caused, and yes, you were pushed into the car in front of you from a stop as you clearly disclose here, and will make very clear to your insurance company as well.
You are free and clear. Get ready to go car shopping.