What a great question! When I first read it I thought it was simple. But thinking about it for a minute I realised I hadn't a clue how to answer, really.
I "know" that light doesn't need a constant input of force to carry on travelling because I "knew" stuff like "we continue to se the light from distant stars even if they no longer exist".
I "know" that light consists of photons that have the property of always moving (in a vacuum) at a fixed speed, which they don't need to reach by acceleration by an outside force becasue they have no mass. For the same reason, they don't slow down. The instant they're formed, off they go at 186000 miles a second, or whatever the exact figure is. And they continue in a straight line indefinitely. (Although they're affected by gravity because gravity is not a force but a variation in the shape of the universe.)
But when you think about it, what the hell does all that mean? Surely anything that moves must have been given energy at some point? As you say, what gives it that initial shove?
What do you google to get an explanation of stuff like this? Or do I need a lifetime of study? If so, it's too late!