White Castle essentially formalized a prior trend of burger vendors at sporting events, state fairs, etc. These were really simple cheap meaty snacks with little more than the patty and maybe some onions cooked on a griddle and slapped on whatever roll they could get from a local butcher. In that sense the WC slider is still fairly true to the original thing.

But, I think it's a bit rich to call it the origin of fast food. Modern fast food in terms of what we think of as technology and business model is a bit broader than that. And just "food you get fast" is obviously far older. The original "fast food" in that sense was getting bread from a baker.