I nervously entered the new classroom. The lights were bright, everything smelled new, and all I could see were the smiling faces of a whole bunch of kids I'd never met. All of a sudden, a tall, well-dressed man joined us in the room, singing at the top of his voice.
"Welcome, welcome, welcome Grade 5!" He sang happily as he winked at me.
I felt, at that moment, that we'd be off to a flying start in no time.
What does the idiomatic expression "off to a flying start" mean in this passage?