Add product to cart with form submit after woocommerce initialized

I am working on a plugin and I am stuck on something.
I want to add a product to cart on submit.
At first I got an error that WP Wasn’t loaded. So I fixed this by using

add_action('wp_loaded', 'wp_after_load');

So here is my code:

HTML

<form method="POST" enctype="multipart/form-data">
    <button type="submit" class="btn btn-primary" name="ws-add-to-cart">Add to Cart</button>
</form>

PHP

if (isset($_REQUEST['ws-add-to-cart'])) {

    add_action('wp_loaded', 'wp_after_load');
}

function wp_after_load() {
    add_action( 'init', 'add_product_to_cart' );

}
function add_product_to_cart() {
        echo '<script>alert("dsa");</script>';
        global $woocommerce;
        global $product;
        $product_ident = $product->id;
        $product_id = $product_ident;


        $woocommerce->cart->add_to_cart($product_id);
}

The thing is, nothing happens.
And my guess is that add_action( 'init', 'add_product_to_cart' ); gets stuck on something, or this isn’t the right hook to use.
I am using this hook to wait after woocommerce is done loading.
Yet I’m not sure if this does what I think it does.
So what am I doing wrong here? I got the code from WooThemes:
https://docs.woothemes.com/document/automatically-add-product-to-cart-on-visit/