[Aiwendil]

Let's actually consult the sources before we get too carried away with speculation. The Ainulindale clearly states that the Children came with the third theme:

Originally Posted by Ainulindale

And they saw with amazement the coming of the Children of Iluvatar, and the habitation that was prepared for them; and they perceived that they themselves had been busy with the preparation of this dwelling, and yet knew not that it had any purpose beyond its own beauty. For the Children of Iluvatar were conceived by him alone; and they came with the Third Theme, and were not in the theme which Iluvatar propounded at the beginning, and none of the Ainur had part in their making.

This statement appears first in the Ainulindale C (the first post-LotR version) and was retained in D and in the published Silmarillion.

In the same text, the second theme is referred to here:

But Manwe was the brother of Melkor in the mind of Iluvatar, and he was the chief instrument of the second Theme that Iluvatar had raised up against the discord of Melkor

The situation as envisioned in the Ainulindale, then, seems quite clear: the second theme represents the efforts of the Valar against Melkor, and the third theme represents both Elves and Men.

However, the situation is somewhat confused in other texts. In LQ2 (the Quenta Silmarillion text from the late 1950s, written several years after the Ainulindale), Men are associated with the second theme:

Originally Posted by LQ2

Little he [i.e. Melkor] knew yet concerning Men, for engrossed with his own thought in the Music he had paid small heed to the Second Theme of Iluvatar

This is the only reference to the themes of the Music in LQ. More is said about the themes in the notes on the 'Athrabeth Finrod ah Andreth', however, which also dates from the late 1950s.

Originally Posted by Athrabeth

This freedom was shown in the Music by His introduction, after the arising of the discords of Melkor, of the two new themes, representing the coming of Elves and Men, which were not in His first communication.

Thus the 'newness' of the themes of the Children of Eru, Elves and Men, consisted in the association of fear with, or 'housing' them in, hroar belonging to Ea, in such a way that either were incomplete without the others.

. . . the Themes of the Children were introduced after the arising of the discords of Melkor.

Christopher Tolkien notes the apparent discrepancy between what is said in the Ainulindale and what is said in the Athrabeth and suggests two possible explanations: 1. The references to 'themes' in the Athrabeth are to related motifs that in the Ainulindale were grouped together as the 'Third Theme'; 2. (which he finds more likely) Tolkien had changed his mind about the themes, and now rather than both being associated with the Third Theme, Elves and Men were associated with the Second and Third themes respectively. This still leaves the statement in LQ2 as something of a puzzle, however, for even in this new conception, Men would still be associated with the Third Theme, not the Second. In any case, one thing does remain clear at all stages: the Children of Iluvatar were not present in the First Theme, the one that Iluvatar propounded at the beginning (and indeed it is an essential element of the philosophy expounded in the 'Athrabeth' that the Children were introduced specifically to rectify the discord of Melkor).