Elect-of-every-race/identification
The Bible gives us no warrant to speak of hypothetical universalism (a universally sufficient atonement--but not universally efficient). This is a speculative doctrine, fraught with problems.
Reading the context:
Paul is speaking (v.1) about all kinds of men. Pray without exceptions (this would be wrong: "that guy/race/occupation I just thought of, I'm not praying for him/them!"). V.4 then speaks of "all men," which in the context surely cannot mean every individual man, but rather a general will that mankind generally, all manners of men, might be saved (thus justifying an indiscriminate gospel call). Finally v.6 indicates that Jesus was given as a ransom for "all"--yes, wider than just Jews, Gentiles too; but I think that Paul is not thinking of "mankind without traditional distinctions" here, but more precisely of the elect-of-every-race. I think this because 1) the blood of Christ has particular application, not general; and 2) in the next verse he refers to his special calling to the Gentiles; the sending of God and the calling of God are each quite particular. We are sent to gather in the elect, we just don't know who they are.