From memory, the most direct and easiest way to influence that would be to use a ‘National Focus’ (NF). Target an ‘Encourage Soldiers’ NF on the region with the highest population within Brazil for the best effect and over time it should encourage Pops to promote to the Soldier type. More indirect means of potentially encouraging Pops to promote to the Soldier type through the use of levers such as wages and taxation usually aren’t as effective as just straight up instituting a NF.
As for Spheres of Influence, anyone who isn’t a Great Power can become Sphere’d by a Great Power so the only true escape is to become a GP yourself. Now, to be fair, becoming part of a Great Power’s Sphere of Influence isn’t necessarily a bad thing and it can certainly come with advantages (such as accessing goods on the global market).