If you need to insert it in an existing page with an already done template you can create a shortcode and a plugin:
create a folder like "your_spa" in the plugin folder of wordpress (/wp-content/plugins/)
create a php file named your_spa.php inside the new generated folder
put this inside the file "your_spa.php"
<?php
/*
Plugin Name: your spa plugin
Description: description
*/
function your_spa_code(){ ?>
<!-- put here your code (this will be inside the body of the page) -->
<?php }
add_shortcode( 'yourspa', 'your_spa_code' );
?>
take care of the links/resources urls (js, json, css): place them anywhere you want them, but remember the path (like in html path => url)
remember to let the apache user read the files (file permissions)
activate the plugin "your spa plugin" inside the wordpress dashboard
use [yourspa] inside a blogpost/page as a shortcut
And now you have created a plugin and a shortcode!
PS: remember that your code will be surrounded by the code of the existing page
It's a little dirty but it's the easies solution.