No, because an unconscious person is not an object or willing
Unfortunately, the RAW answer ("rules as written") to your question is "no." As you said, the rules about the Thunderstep state (bold added to emphasize):
You can bring objects as long as your weight does not exceed what you can carry. You can also teleport a willing creature of its size or smaller that carries equipment to its carrying capacity.
Then the ally must be "objects" or "a willing creature" for teleports.
Your unconscious ally is not an "object"
Although an unconscious creature behaves like an "object" (since it does not move), the Dungeon Master's Guide defines an object on page 246 as (bold added):
a discreet inanimate Article.
And "inanimate" means more than "not moving": it means "not alive" or "lifeless." So your unconscious ally is not an object (not a collection of objects).
Your unconscious ally I can not he says he is "willing"
I am sure that the player who controls your ally He is totally "willing" to teleport his character: he can save the character's life and it's amazing to boot. But the character itself is unconscious. And it has been said elsewhere that an unconscious person cannot be "willing." Even if this is something they would consent to if they were aware and capable, at this moment they cannot consent to anything since then (PHB, p. 292, bold added)
An unconscious creature … is not aware of its surroundings.
Therefore, an unconscious ally, who would normally agree with your teleportation, does not know that you are trying to do it or why, and therefore cannot have any opinion on whether you should do it or not. Even if they previously gave you general permission to teleport in this precise scenario, they are currently not in the mood to be "willing" for you to perform such an action. So, in this (and in all other) contexts, You cannot say that an unconscious creature is "willing."
A DM could let your ally become briefly arranged
A DM can bend these rules if they wish! The ability to teleport an ally to security is really great, and the DM could easily decide that this is allowed (perhaps stating that the ally flies to consciousness only for a second and becomes willing). But if we strictly follow the rules as written, Thunderstep cannot teleport an unconscious person, such as An unconscious person is neither willing nor an object.