You can done this by edit the following file
vendor/magento/module-checkout/view/frontend/web/js/checkout-data.js
In this file you can edit the getShippingAddressFromData: function (){ .... }.
The code for get existing address details are
var customerData = window.customerData;
var customerAddress = customerData.addresses[0];
$('[name="company"]').val(customerAddress.company)
$('[name="city"]').val(customerAddress.city)
$('[name="postcode"]').val(customerAddress.postcode)