There are more than 2 sides with nukes. A pre-emptive strike would not prevent all the other countries from retaliating.

While first strike sounds good, don't forget that there are nuclear subs everywhere in the world, at all times, just waiting for the word.

Sure, but my point is that, from China's perspective, they don't have the opportunity to validate that the swarm of missiles coming their way aren't nuclear. They have to assume that they are or they risk losing a large amount of their retaliation capabilities.

So to answer the question

> Would the US be willing to launch a bunch of non-nuclear missiles to China

No, because China has to treat them as nuclear either way.