There isn't just one Compact of Free Association -- there are three. All of the freely associated states (Federated States of Micronesia, Republic of Palau, and Republic of the Marshall Islands) were previously part of the Trust Territory of the Pacific Islands, of which the current Commonwealth of the Northern Mariana Islands was also a part. All of those islands were captured by the US military during WWII. Before that, they made up the Japanese-administered South Seas League of Nations Mandate.

The Trust Territory of the Pacific Islands was administered by the United States under the United Nations. Trust territories were supposed to be temporary arrangements by which some Allied power would rule an area captured by an Axis power and "prepare it for self-governance." The US military did want the TTPI to continue on as a US territory (for something it called "strategic denial" meaning not letting any other power take the region). However, it was constrained by international and local pressures to hold a plebiscite vote for people to choose their own political status. Over the course of the negotiations that led up to that vote (which didn't happen until the 1970s), the TTPI broke into four units -- largely on the basis of what extra funding those units thought they might be able to secure post-independence. The Marianas voted for Commonwealth status. The other units voted for free association.

Guam was right next to all of this, but it has a different political relationship to the US and so none of the international pressures that spurred the US to (finally) get around to holding plebiscite votes here applied in Guam. Both it and American Samoa have been US territories since the very late 19th century, and neither was deeply involved with the TTPI.