When you go to Cart on Woocommerce the Shipping Calculator only shows the title and then reveals options only when clicked. This means it can easily be missed. The following code can be used to display it completely.

Simply paste the following into your custom CSS section:

section.shipping-calculator-form {
display:inline !important;
}

If you want to hide the State option and zip/post code option add this CSS as well.

input#calc_shipping_state, input#calc_shipping_postcode {
display:none !important;
}