The Taiwan issue is a bit complex, but I'll try to be concise and stick to the invasion idea. The problem for that to happen was timing - the Chinese Civil War happened at a really eventful period in East Asia. For context, we have to go half a century back.

In 1895 the Chinese were beaten by the Japanese and with the Shimonoseki treaty Japan gained control of Taiwan, known as Formosa at the time. They controlled the island till 1945, when it was taken by the US forces and in the same year they gave the administrative rights to the island to the ROC government, until a peace treaty with Japan would be signed - which would only happen in the San Frascisco treaty in 1952.

In 1949 the ROC lost the civil war and relocated their government to Taiwan, but legally, the island was still owned by the Japanese and housed US forces. Attacking the island would've involved the PRC into a messy international conflict and another problem came to be - the Korean war. With the war requiring more attention, the Taiwan problem was left on the back burner and by the end of the war the Western world saw the communist movement as a real threat. The US already had good diplomatic relations with the ROC, and by 1954 they had an extra incentive to support them against the PRC. A defensive treaty was signed, in which the US promised to protect the island and come to aid if and whenever PRC would attack. That took the military action out of the question, and from then the issue became a diplomatic one.

Basically, the PRC had a really small window of time to try an invasion, but then the Korean War happened. In a way, the war acted as a proxy of what a conflict with a US backed ROC would look like, while also hastening the cooperation between the two. Hope I answered your question and didn't make a lot of mistakes, English isn't my native language :)