Or try using creme fraiche. It's a similar (very) taste to sour cream, but lighter in texture.

You can thin the sour cream by mixing it with a bit of whipped heavy cream (unsweetened)
Yeah, it's kinda of gilding the lily, but it works.

Unfortunately the laws of physics will apply; it will only float atop a really thick soup.

If it's not a pureed soup, but one with chunks, e.g. of veggies, you could strategically push a little of the solid stuff to the center and sort of sit a dollop of sour cream on top of that. (At least you could if you have far more patience for fiddling than I do.)

Another idea - you could thin the sour cream a little, then use a squeeze bottle to swirl it over the soup's surface - that way, its lighter weight might allow it to float.

Or, serve the soup in a wide, shallow bowl so when the sour cream sinks, its peak sits a bit higher than the surface - like an iceberg breaking the ocean's surface.

(Clearly, I'm in heavy work avoidance today - and pondering the physics of sour cream is a good distraction.)

You need a fairly thick soup and probably less sour cream.