Question:

How are we considered "chosen" if G‑d first offered the Torah to other nations?

Answer:

The Midrashic account1 that G‑d first offered the Torah to all the other nations, who rejected it, before offering it to the Children of Israel, who promptly and unequivocally accepted it, must really be understood on a deeper level. From the very beginning, G‑d chose Abraham's descendants to be the Light unto the Nations. Indeed, from the very beginning of time, the Jewish people were chosen to receive the Torah.

Nevertheless, G‑d offered the Torah to the nations, so that they too would have the opportunity to accept the Torah if they so wished. At the same time, G‑d knew that the nations would refuse the gift. Thus, it was clear that G‑d was being "fair," and the nations no longer can protest that they would have liked to receive the Torah.2

[Now, this certainly begs the question: if G‑d knew that they would refuse the Torah, wasn't the act of offering it to them a sham? See If G‑d knows the future, how can we have Freedom of Choice?]

I am sure this can be understood on deeper levels as well, but I hope this helps.

Chana Weisberg for Chabad.org