The lifecycle is more complex than this. Slash and burn agriculture is used to squeeze a few cash soybean crops out, this requires specific GMO soy, and these are 90% sold to China to fatten pigs.

When the land is only suitable for grass, it's grazed for awhile, after which it's basically desert.

South America also has some of the richest cattle land in the world in the Pampas, which has sustained beef production for hundreds of years on land which is otherwise unsuitable to food production.

Pressure on one company could stop the conversion of rainforest into soybeans. This doesn't solve the problem in a single stroke, nothing can, but it would help, and it doesn't require influence over the government of Brazil.