I have an old let's encrypt (but disregard that, it could be any) certificate that is no longer active.
How may I check if it was valid at the time?
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The validity of a certificate can be shown by any tool that can parse / decode X.509 certificates:
openssl x509 -text -in <certficiate.cer>
You may have to add
-inform DER if your certificate is in binary form instead of PEM (base 64 text with header and footer lines).
Validity Not Before: Mar 31 09:10:51 2020 GMT Not After : Mar 31 09:20:00 2021 GMT
The validity period is in between the
notAfter fields that are mandatory for any X.509v3 certificate.
If you want to check if the certificate was valid according to the CA you may want to check the revocation status as well. Usually that means that you need to provide CRL (Certificate Revocation List) files.
You could perform a full verification check with chains and whatnot by using:
openssl verify -verbose -attime <etc>
If you do not have access to the CRL's then you cannot say for sure if a certificate was valid a the time.