You could implement the UPS shipping quote server behavior on your cart page to get back a quote value before the user checks out. To get a proper quote though with the shipping quote server behavior you may need to provide a full ship to address rather than just a zip code. You could add a ship quote form to your cart page set the trigger for the shipping quote server behavior to be based on the submit button being pressed in this form.
You can apply this server behavior by going to Server Behaviors > eCart > shipping.