I want to change the text at the checkout page below the returning customer bar, namely "If you have shopped with us before, please enter your details below. If you are a new customer, please proceed to the Billing & Shipping section.".
The text seems to be present in: plugins\woocommerce\i18n\languages\woocommerce.pot
and plugins\woocommerce\templates\checkout\form-login.php
I know I can simply adjust the text in those files; but if WooCommerce gets updated it will be overwritten.
Is there a way to change this text with hooks, although the text doesn't appear in my theme?
I don't want to use a plugin for this if possible.
When Overriding Woocommerce templates via a child theme (or a theme) you will not loose any changes when Woocommerce plugin is updated.
So in your case, as explained on the comment of the template checkout\form-login.php you will have to copy this file to your child theme:
/**
* Checkout login form
*
* This template can be overridden by copying it to yourtheme/woocommerce/checkout/form-login.php.
Woocommerce templates are made to be overridden via a child theme (or theme)