Hi there,
I would:
1. Download the GP Child Theme zip:
https://generatepress.com/api/themes/generatepress_child.zip
2. Open the zip files styles.css and functions.php files in my IDE on my desktop. I use Visual Studio Code but there are plenty of others like Atom, Sublime, XCode, Brackets.
2.1. Copy my current sites CSS to style.css
2.2. Copy ONLY the custom PHP from current site to functions.php
3. Zip the Child Theme folder back up.
4. Remove the Custom Functions and Styles from the current site.
5. Install Child Theme, make any fixes such as updating Logo and footer bar copyright info.
For peace of mind i would suggest using a Staging server to make the changes to the live site.