You can always create a server action, with a website url that do it.

By default we avoid since it allow anybody to update your cart. But in your case, seems to be what you want...

New Server action > website_path > add2cart

A model writable for public user: e.g. Custom View

Code:

sale_order = request.website.sale_get_order(force_create=True)
sale_order._cart_update(product_id=int(request.params.get('p')), add_qty=1)
response = request.redirect('/shop/checkout?express=1')

And now you can create link to your odoowebsite.com/website/action/add2cart?p=