Light always travels at the speed of light. It never increases or decreases its speed. (Technically, this is only true when the light is in vacuum, but the air in a room where the light is turned on is sufficiently close to a vacuum.)
You're thinking about light as a classical particle, which indeed has to start from rest if it wants to move. Instead, think of light as a vibration of the electromagnetic field.
There is a simple analogy for this - without any quantum mechanics or relativity, just classical mechanics.
Consider a string attached to a wall on one side and held by you on the other side. If you vibrate the string on your side, the vibration will propagate to the other side at a fixed speed that depends on the material from which the string is made and on the tension of the string.
The propagation speed of the vibration of the string does not start from zero, nor does it increase or decrease at any time. It is always constant.
Similarly, light is a "vibration" of the electromagnetic field. This vibration always propagates at a constant speed c.
- Barak Shoshany, Graduate Student at Perimeter Institute for Theoretical Physics
Listen to my commentary on this