According to Lauren McDaniel at UCLA's special collections library, Susan Sontag's papers (so far at least) do not contain any writings dated 1960. It's possible that new batches of material coming into that collection will eventually include some stuff from our year. Her career as writer really began in '62 and she published just a few things before that. It's known among Sontagians (and perhaps less so about Rieffians) that Susan was an uncredited quasi-co-author of Philip Rieff's The Mind of the Moralist (1959).
There is a piece dated 1960: it appeared in the Supplement to the Columbia Dailiy Spectator on November 18, 1960, on pages 3, 4 & 8: "History in the Drama." Sontag was an instructor in religion at Columbia.
I procured a copy of this piece. It's a review of Tom Driver's The Sense and History of Greek and Shakespearean Drama published by Columbia University Press. This is almost fully mature Sontagian writer at the level of the sentence--without, unsurprisingly, the pure verve of the writing on camp and avant-gardism coming soon. Driver's book, she says, contributes to a number of current debates - among them "the clash between an orientation to psychology and an orientation to history. The 'linear' view is under heavy attack by contemporary psychology-minded intellectuals. It is said that we have seen 'the end of ideology,' the end of hopes for radical transformation of the human condition, and that political convulsions are precisely the fruit of th[e] misguided and presumtuous energies of Biblical messianism."
She is here referring to a major book of 1960 by Daniel Bell: The End of Ideology. And she's in part using the Rieffian approach to and critique of "contemporary psychology-minded intellectuals" to counter the centrist/post-ideological End of Ideology thesis, which in part attributes the politics of difference (ideological critique of the American suburban middle-class 1950s-style status quo, for instance) to psychological maladjustment and crazy egoistic desires.