Is it true that your first job defines you?

A supervisor of mine recently said, "If you don't go for big tech now. You won't be able to change your mind later. If you start small, it'll be very hard to break through into bigger opportunities."

I'm wondering if it's true, because I'm not sure if I want to work in big tech but I might change my mind later on in my life. I will soon be a new grad and I'm concerned that if I choose to "start small", then I'll put myself in a box later on.

What do you think? Is that statement true? Should I aim big from the get go if that's where I would eventually want to be?