After some investigation, I've come up with a solution. In order to achieve the desired outcome, you must dynamically generate a script tag and then attach it to the head of your document:
export class Widget {
//...
injectScript() {
let element = document.createElement('script'); // create the script tag dynamically
element.src = ''; // specify the source (insert URL within quotes)
element.type = 'text/javascript'; // define the type of script
element.async = true; // enable asynchronous execution
element.charset = 'utf-8';
// append the script tag to the document's head
document.getElementsByTagName('head')[0].appendChild(element);
}
initialize{
injectScript();
}