Wordpress REST API issues

I am trying to update a user's role through an jQuery ajax call. The ajax sits inside a certain page and runs when a user is redirected to that page -> (http://helpgrowusacom.staging.wpengine.com/paid-setup/). The script itself pulls in the ID of the current logged in user in order to issue the update request to the right endpoint/resource. To test it with a random user the details are -> username: advisor002, password: hgusa123 (or HGUSA123) .
So right now when the call happens it returns a 403 forbidden error. Here is a gist link which shows the script itself ->
It is a POST request and I understand lack of authentication is perhaps the culprit. After some Google-searching the only suggestions I found were to install the WP REST API v2 plugin, as well as this plugin (https://wordpress.org/plugins/oauth2-provider/) , in order to fix the authentication. I was hoping to see if there is a solution that does not require installing multiple plugins.