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I made a note, how to solve the error "The response is not a valid JSON response." by Google Site Kit plugin initial setting at WordPress.
In my case, the problem was WAF(Web Application Firewall).
So, until I had completed the Google Site Kit initial setting, I temporarily stop the WAF.
And the problems solved.
After Google Site Kit plugin initial setting completed, I restart the WAF and Google Site Kit settings working fine.
It seems that there are other solutions like "reload several times", "Stop wordpress security plugins, until Google Site Kit initial setting completed".
Please refer to Google's official page for other error handling methods.