"Nosotros vamos a aplicar para ser maestros."
"aplicar" is wrong to use in this case because it is more of an application of a direct object. also to ask for a "solicitud" is generally more appropriate. Using this "cognate" is wrong and is like using embarazado to mean embarrassed. this just highlights the lack of understanding of the spanish language of a language of its own but rather having it compared to english and having english be superior.
Shouldn't this be "suplicar"? "Aplicar" has a connotation of direct and physical application (like suncream).
I've never heard 'aplicar' to mean this (rather 'pedir' or 'solicitar' and a quick glance in the dictionary sheds no new light on it. Is it a regional thing? I can certainly imagine it being used in places where Spanish is in contact with English, but what about elsewhere in Latin America?
Según mi experiencia, se usa "solicitar" mucho más, y a veces "postular" o "pedir".
mousing over para yielded "in order to" in the hints. You can do that right here at the top of this page. That little triangle extends the list.