TL;DR: Since the idea of tinoq shenishba is an example of compulsion, and it's absurd to think that someone is punished for something they were compelled to do, there must be a concept of non-Jewish tinoq shenishba. That said, a good number of Noachide Laws are self-evident; eg there is no tinoq shenishba when it comes to outright murder.
Tinoq sheNishba is more of an example than a status. The source gemara is Shevuos 5a, from a discussion of a case in the mishnah, of someone who entered the Beis haMiqdash not knowing they were tamei, and found out while there. What about if he didn't know what tum'ah was? Here's the quote with R' Shteinzalts's commentary:
א"ל רב פפא לאביי? אלא דקתני אין בה ידיעה בתחלה ויש בה ידיעה בסוף, מי איכא דלית ליה ידיעת בית רבו? א"ל: אין משכחת לה. בתינוק שנשבה לבין הנכרים:
Rav Pappa said to Abaye: But [how can you explain the halakha] that is taught [in the mishna: For cases in which] he did not have awareness at the beginning but had awareness at the end? [According to your explanation,] is there [anyone] who does not have [the elementary] knowledge [of the halakhot of ritual impurity that he gained] from his school? [Abaye] said to him: Yes, you find it in the case of a child who was taken captive among gentiles[, who never received even the most elementary level of knowledge].
We see the law is about someone who never knew that something was prohibited. The constrast there is to people who once know, and forgot. Or knew for step A and step C, but forgot during the middle step B.
This kind of ignorance is a case of oneis, being forced to sin. It is just that for well-known laws, as tum'ah was in the days of the Beis haMiqdash, the example case was someone who was raised in captivity and therefore didn't have a basic education or even cultural osmosis of the basic laws.
The actual rule is "אונס רחמנא פטריה -- The All-Merciful pardons the one compelled". In Avodah Zara 54a, Rav Zeira says the source is the verse "ולנער [וְלַֽנַּעֲרָה֙] לֹא־תַעֲשֶׂ֣ה דָבָ֔ר -- and to the girl, you shall do nothing." (Devarim 22:26). A betrothed woman who has an affair is punished, but here Hashem adds that if she were a rape victim, she is not.
With that background, I think we can get to your question. As we see from the Jewish case, the leniency accorded such ignorance is because the sin is considered under compulsion. So, the only way a non-Jew who is a tinoq shenisba could be held punishable would be if a non-Jew who is forced to sin were punished for sinning. Such as if the Torah would expect the execution of a non-Jewish married rape victim. Which I am sure you agree would be absurd.
Now for the logistic problem: Which of the 7 laws need teaching?
That stealing and murder are bad is self-evident. Even among murderous thieves; they feel the "energy" of breaking taboo. But abortion, while not murder (in most opinions) is also under this umbrella. Wouldn't be known without proper upbringing.
Rav Elchanan Wasserman Hy"d zt"l (Maamar al haEmunah) says that believing there is a G-d is self-evident, and only desire pushes people to rationalize not accepting the obvious. This itself is not self-evident to me. But if so, belief in G-d and avoiding blasphemy would also not be subject to tinoq shenishba treatment, simply because it can't happen.
Avoiding idolatry is not necessarily self-evident, even according to R' Elchanan. There are many religions that believe in a Creator and Ruler, but also worship middlemen and helpers. So, I guess someone raised Mormon could be a tinoq shenishba with respect to their teachings about the Godhead.
Illicit sex? I suppose it would depend on which kind. But had you asked in the 1950s, I bet I would have assumed that homosexuality being a sin was self-evident. Time proved me wrong. In any case, I don't think someone raised in a community that has marriage needs to be taught that marital infidelity hurts. Even among "swingers" (like what I wrote about murderous thieves), knowing they're breaking taboo is part of the allure the promiscuity has for them.