Becasue the distance that the electrical signals have to travel is small compared to a billion light years.

The signals which are from sight are electrical, i.e charges are accelerated through your nervous system to very hight speeds but it has to travel a short distance. If your eyers where located lets say 5000 mies from your brain it would take much much longer for you to be aware of what you are looking at at a specific instant in time.

Light is fast but if the distancee is great greater and greater the time for it to arrive would be longer and longer