I really like how you’ve put this beginning together. You’ve introduced your characters simply and by showing them doing something, preparing for something. You give us little bits of information, but leave out just enough to keep us expectant to what’s going to happen (in the next few lines and in the rest of the story). Beginnings are hard, and I like how you’ve done this one.
Also, I don’t know if you did it on purpose, but I like that you have the POV character DRIVING the car. It’s a good, subtle, visual metaphor that shows that she’s literally steering the story as it moves forward.
There’s not actually "wrong" with this sentence, it’s just a little clunky to have the description of Matthew’s action buried inside the description of the tires. It might work a little better if you break it into two sentences (maybe do Matthew’s action first, then do the description of the tires’ noise, which I actually like a lot).