Seven Mitzvot of Benei Noach without Na'aseh veNishma

Question

Why are Benei Noach obligated in their Seven Mitzvot if they never said Na'aseh veNishma?

Answer 1

Because it wasn't put to them as a choice, but unilaterally imposed on Noach and his descendants by G-d. Being human carries basic obligations, because humans have abilities animals do not and a corresponding charge that animals do not: basic maintenance of the world (the Jewish understanding of the word often mistranslated to English as "subdue").

Answer 2

It seems from the gemara (Hullin 92a bottom line) that they did indeed accept commandments upon themselves. The gemara uses the phrase:

שלשים מצות שקבלו עליהם בני נח
Thirty commandments which Bnei Noach accepted upon themselves.

Answer 3

Because it is a much more basic covenant than that which exists between G-d and Bnei Yisrael. The latter is based on mutual responsibility and chosenness. G-d chose Bnei Yisrael for a particular mission. He also chose them as His protected people because of the actions of their fathers. If Bnei Yisrael abide by G-d's commandments, which are set up in such a way as to mark them as a priestly and princely nation, with heavy responsibilities as well as certain privileges, then G-d will protect them in their land and provide them with their needs. But they have to be worthy of this role.

Contrast that with the covenant between G-d and Noaḥ. G-d promised not to destroy the world. Bnei Noaḥ just have to be decent people (from the Biblical perspective, the 7 Noahide Laws are a moral code, not a legal one like the Torah - this includes recognizing and not cursing G-d, btw). All Bnei Noaḥ must be worthy of, then, is not to be destroyed. And since it was a unilateral covenant, even if they become depraved again, G-d promised not to destroy the entire world as a result. Sedom and 'Amorah demonstrate, however, that micro-level destructions for depravity are still fair game.