WooCommerce – Echo ID of Variable Product Default Attribute

I am trying to dynamically echo out the ID of the default attribute for variable WooCommerce products.

Using $default_variation = $product->get_default_attributes(); so far I am only able to echo out an array of attributes for each variable product.

Is there a WooCommerce method available, as opposed to get_default_attributes, that will simply echo out the ID of the one default attribute?

Alternatively is there a method I can use in my function, included below, to cycle through the array and echo out only the default attribute ID?

function add_new_add_to_cart_button() {
    global $product;
    if( $product->is_type( 'variable' ) ){
        $product_id = $product->get_id();
        $default_variation = $product->get_default_attributes();

        echo '<form class="cart">
        <input type="hidden" name="product_id" value="'.$product_id.'">
        <input type="hidden" name="variation_id" value="'.$default_variation.'">
        <input type="hidden" name="qty" value="1">
        <button class="button product_type_variable add_to_cart_button" style="float:none;" type="submit" name="add-to-cart" value="'.$product_id.'">Buy Now</button>
        </form>';
    }
}
add_action( 'woocommerce_after_shop_loop_item', 'add_new_add_to_cart_button', 15 );