Considering the Post-WWII policy towards communism and the establishment of relations and a huge amount of aid delivered to Taiwan it's difficult to call it a "lost Chance."

That said, it very much depends on what one defines as Sino, as in the late 1940s, the US did not really consider mainland China as governed by the Chinese Communist Party, "Chinese." If we are operating under the assumption that the Republic of China (Tawian) equates to Sino-American relations then the answer is that the Americans missed no opportunities.

Now if one were to talk about mainland China, then things get rather complicated considering that the US until Nixon didn't even recognize the Communist Chinese government.

Furthermore relations between the Chinese and the US were rather strained for quite a long time. That said, whether or not the scorecard went as far back as the Opium War very much depends on who at the time was keeping count. Certainly much of the goodwill that may have been garnered by the US during WWII probably evaporated for the Communist Chinese when after WWII the US refused to acknowledge them. Not to mention the rather distinct lack of effort that the Chinese had received during the Second-Sino-Japanese War until a good way into it.