It is very well possible that God intervenes physically to prevent accidents. But He can do that also by simply intervening in the spiritual domain (the soul).
The soul interacts with the human mind, and God mainly interacts with mankind through the soul. By influencing the soul of people, God also influences human actions and their influence on the physical world. No physical miracles are needed in this manner of God influencing things and communicating. Importantly, God also communicates with and influences humans on a spiritual level, in a relationship with Him.
The influence through the soul could have major consequences, like in influencing the mind of human rulers for example, or in steering ‘coincidences’. Let’s suppose the following: Mr. Miller is seriously injured in a car accident. He was a pedestrian at the time, and the driver was nervous and distracted because he was in a hurry. He was in a hurry because the lady in the store, who was supposed to have packed his purchase as a gift for his wife, had forgotten to do so while he was doing other purchases and did not have the gift ready when he re-entered the store. Now let’s turn the story around. God feels compelled to give the store employee a subtle mental clue through which she reminds herself that she has to pack the gift for the gentleman while he makes some other purchases. The gentleman then is not in a hurry on his way home, and not distracted. He does see Mr. Miller and stops. Mr. Miller does not get hurt. Why did God give the store employee a subtle mental clue? Someone had prayed for Mr. Miller than he would be protected from harm. God steered ‘coincidences’ without suspension of physical laws. A prayer was heard while no miracle occurred.
You might ask, why then does God not prevent all car accidents? Or while we’re at it, why not prevent all earthquakes, landslides, wildfires, cancers etc.? Everything has its natural order, and in that case the natural order would be overthrown. Analysis suggests that constant intervention of God in the natural order would eventually have to have Him go to such lengths that then even the outcome of human actions would be unpredictable, i.e., one could not know what to expect from one’s own actions. Also, we might live in a nice Disneyland world, but it would become pointless after a while, since it does not allow for growth, progress and virtue through adversity.
The last paragraph should also be an answer to God preventing natural disasters. If you really believe God does prevent them, I have a simply question for you: why then did He not prevent the tsunami in Japan?