We don't disclose account information or validation details in most cases, but I hope this will help:
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The "Not Before" date/time you see in crt.sh is exactly one hour before the certificate was successfully requested and issued. (This is to accommodate clients with clocks that are off by one hour, which is common in places that observe Daylight Savings Time.)
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I happen to know that Network Solutions' "domain parking" service does use Let's Encrypt certificates. If you registered your domain with their default settings, their system very probably requested the certificate as part of adding your domain to parking.
If there's a suspicious certificate that really doesn't seem like it could have been issued by a hosting/domain/CDN/SaaS provider you use, then there is a direct contact for you to report the details so we can investigate. In almost every case, though, we find it's a hosting provider and respond with a template that's just the information above.