No, because an unconscious person is neither an object, nor willing
Unfortunately, the RAW ("rules as written") answer to your question is "no." As you stated, the rules on Thunderstep state (bold added for emphasis):
You can bring along objects as long as their weight doesn't exceed what you can carry. You can also teleport one willing creature of your size or smaller who is carrying gear up to its carrying capacity.
So the ally must either be "objects" or "one willing creature" for you to teleport them.
Your unconscious ally is not an "object"
Although an unconscious creature behaves much like an "object" (in that they do not move), the Dungeon Master's Guide defines an object on page 246 as (bold added):
a discrete inanimate item.
And "inanimate" means more than "not moving": it means "not alive" or "lifeless." So your unconscious ally is not an object (nor a collection of objects).
Your unconscious ally cannot be said to be "willing"
I'm sure that the player controlling your ally is totally "willing" for you to teleport their character: it might save the character's life, and is awesome to boot. But the character itself is unconscious. And it has been stated elsewhere that an unconscious person cannot be "willing." Even if this is something that they would consent to if they were conscious and capable, at the moment the cannot consent to anything since (PHB, p. 292, bold added)
An unconscious creature ... is unaware of its surroundings
So an unconscious ally, who normally would be totally fine with you teleporting it, does not know you are attempting to do so or why, and thus cannot have any opinion on whether or not you should. Even if they previously gave you blanket permission to teleport them in this precise scenario, they currently are not in the state of mind to be "willing" for you to do such an action. So in this (and all other) context(s), an unconscious creature cannot be said to be "willing."
A DM might let your ally become briefly willing
A DM might bend these rules if they want! The ability to thunderously teleport an ally to safety is really cool, and the DM could easily decide that this is permitted (perhaps declaring that the ally flits into consciousness just for a second and becomes willing). But if we're going strictly by the rules as written, then an unconscious person cannot be teleported by Thunderstep, as an unconscious person is neither willing nor an object.