Mi Casa es tu Casa
Any country is exiled in Mexico
In order for Mexico to host an exiled country, it has to be Democratic, and the faction leader needs to be Democratic. Although Mexico does not have to be the faction leader, it still needs a powerful army or economy to host exiles.
Head straight to the Women's Suffrage focus to change ideology to Democratic. Rush to Arrest General Cedillo to prevent a civil war and take democratic advisor in between, DO NOT take Institutional Revolution yet. Take the Spanish Civil War Refugees focus to get create South American faction. Depending on Mexico's relation with church, take Falangist Veterans or Support Spain's Loyalists to avoid civil war. Realpolitik is a dead end in the focus tree and will not lead to war goals against South American nations. After the faction is created, take Institutional Revolution to turn Democratic, and lower tension requirement by guaranteeing. To increase world tension, take March Southward to get more territory. Once world tension reaches 25%, check the European situation and guarantee countries that under Axis threat. For example, it is recommended to guarantee Finland because the European nations may join the allies instead. Wait for Soviet Union to declare war against them and answer their call to arms and invite them to the faction. To ensure that the war target will not capitulate and give a peace conference, Mexico may need war participation. One strategy is to declare on a neighboring country while at war. They will join the opposing faction. Capitulate them to gain war score. However, it may be sufficient to merely send some units in an effort to try to help out. As long as Mexico is neutral with respect to the war between Germany and the Allies then any units from Mexico will be able to pass through the Danish Straits, even if Germany has already taken control of Jutland and Østlandet. Furthermore, the faction may be formed with just Finland, once Mexico answers the call to arms. Wait for Finland to capitulate thus making them an exiled country in Mexico