If you can access your domain through Google, then just make the DNS records there. You wouldn’t need to transfer the domain to SquareSpace. I only originally mentioned SquareSpace because you said you didn’t have access to the DNS records via Google (so I assumed - probably incorrectly - that the domain was with SquareSpace instead of Google, based on the ‘whois’ lookup that says SquareSpace).
Anyways, if you can access the domain via Google, then here are the steps for editing DNS records via Google: https://support.google.com/domains/answer/3290350?hl=en