Yes,the Customizer settings will not carry over from parent to child. Activating a new child theme essentially means you are starting from scratch with regards to the Customizer.
Perhaps, try cloning the site and run it on a development server or local machine, and make the switch, then see what is lost.
I did find a free plugin that i tested out, and successfully exported and imported the customizer settings on the twentyseveteen theme/child theme. Super easy. Maybe give that a try.
Customizer Export/Import
https://wordpress.org/plugins/customizer-export-import/
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