Trying to show products from API instead from database

I want to fill the webshop with products from my API and not from the WordPress database.

So I’m doing a HTTP GET request to get my products, which gives me the following response:

[
    {
        "id": "1",
        "name": "Product 1 from API"
        "price": 1,
        "vat": 19
    },
    {
        "id": "2",
        "name": "Product 2 from API"
        "price": 1,
        "vat": 0
    },
    {
        "id": "3",
        "name": "Product 3 from API"
        "price": 2,
        "vat": 21
    }
]

Now I gladly want to use that data to show it on the shop page. Without inserting it in the WordPress database. But I don’t know how.

I have already tried the following hooks:

woocommerce_before_shop_loop
woocommerce_before_shop_loop_item
woocommerce_before_shop_loop_item_title
woocommerce_shop_loop_item_title

Unfortunately that didn’t worked out.

Currently I have this:

Link to screenshot: http://imagizer.imageshack.us/v2/1645x944q90/923/VEYldV.png

But the products “brood”, “kaas” and “vis” came from the WordPress database which I don’t want.