Taxonomy hierarchy via separate dropdowns
You probably won't be able to do that without some custom code.

An existing module for the purpose is Simple hierarchical select:


  Simple hierarchical select defines a new form widget for taxonomy
  fields to select a term by "browsing" through the vocabularies
  hierarchy. The widget is available in node forms and as Views exposed
  filter. 


https://www.drupal.org/project/shs

There is also the more full featured module Hierarchical select