Did Paul say this includes everyone that was ever conceived? No. Is there anything in the context that would support the idea Paul is talking about everyone that was ever conceived? No.
I must respectfully disagree. Paul appears to be purposely employing language that would apply to all men universally. In verse 12 he writes "there is no distinction between Jew and Greek." This is a way of saying "this applies to everyone."
When he writes "Whoever will call on the name of the Lord will be saved" in v. 13, there is a positive assertion. Those who call on the name of God are saved. There is no room within such a statement to read into it and see that there is some other way to be saved other than believing in God.
Then, in v. 14 makes it clear: "How then will they call on Him in whom they have not believed?"
The question is posed as a problem. Paul is essentially asking, "How can they be saved if they don't believe in Him?" It is a rhetorical question with an easy answer: "they can't." He then follows this up with, "How will they believe in Him whom they have not heard?" This verifies that "they ca't," but that "they won't" apart from preaching.
I really don't see how else we can interpret this. Unless such an interpretation clearly contradicts another part of Scripture, I feel that we are compelled to read Romans 10:12-14 at face value and apply its understanding to other parts of Scripture, because I don't think it contradicts any of it.
As I have shown there are other verses that suggest Gentiles were treated differently: Ro. 2: 15 They show that what the law requires is written on their hearts, while their conscience also bears witness and their conflicting thoughts accuse or perhaps excuse them
That is a difficult verse, but what does Paul follow up with in Rom 3 "There is no one righteous, not one, there is none that seek God." So ROm 2:15 isn't explaining to us an alternative way to be saved, it explains how men are morally accountable apart from the Law. They do both good and bad, but violating God's Law or owne's own conscience just once is equivalent to committing cosmic treason against God. Apart from this understanding, I don't think we appreciate how sinful all of us are and how much all of us need God's grace.
Ro. 5: 13 sin indeed was in the world before the law was given, but sin is not counted where there is no law.
This is where context is key. In Romans 10:12-14, you address that we should look at context. However, the context does not lead us to different explanation than my own. But, how about Romans 5:13? The very sentence before states, "Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned." So, one thing we do know is if all men sinned from the time of Adam, Romans 5:13
is not saying that we are not sinners apart from the Law.
What Paul is referring to is a much more difficult concept that he returns to in Chapter 7, which is how "through the commandment sin would become utterly sinful" (Rom 7:13). The Law increased the offense of sin, but it is not that sin didn't already exist. In Rom 5:14 it states, "Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam." Sin in the likeness of Adam refers to those breaking commandments God has given. So, we can sin like Adam when we knowingly break one of God's commandments, but we can also sin when we do something wrong where there is no specific commandment to address it.
Much of this is a topic for another discussion. However, how can I be confident that my exegesis is right and yours is wrong? I do think internal consistency plays a large role in revealing who is right on this one. I can believe all these different verses and my interpretations don't require me to disregard a verse or make it say something it does not say. IN fact, the dots all connect.
However, if we cherry pick a few verses out of the Bible and come up with an exegesis that there are two ways to be saved, one by works if we don't know any better and another by faith in Christ, we just torn the whole Bible into shreds and we have to avoid such a reading, as it forces us to completely disregard clear statements to the contrary. Ultimately, we would be forced to be intellectually dishonest if we were to hold to the inerrancy of Scripture, but find that certain verses that don't fit how we see things just can't be true.
We are following for the most part in the Old Testament individuals and to some extent the nation around these individuals. We are not following other nations but do get some glimpses like with Jonah and the city of Nineveh, so did God make himself known to the people in Nineveh?
Granted, there are specific situations where God shows His mercy on gentiles, but what you posit is that there are stories of God's grace to the gentiles that are not recorded in the Scripture and that these gentiles are saved somehow. However, based on Scripture, how can we come to this conclusion? We have no indication of this.