The only document to rely on that an entity has been independently assessed as complaint is an Attestation of Compliance, which is a formal document completed by a Qualified Security Assessor (QSA). It is a few pages long. As @Bobson says, you can validate the status of the QSA that carried out an assessment here.
https://www.pcisecuritystandards.org/assessors_and_solutions/qualified_security_assessors
A 'certificate' is a worthless piece of paper. The PCI SSC has an FAQ describing why.
https://pcissc.secure.force.com/faq/articles/Frequently_Asked_Question/Are-compliance-certificates-recognized-for-PCI-DSS-validation
The only documentation recognized for PCI DSS validation are the
official documents from the PCI SSC website. Any other form of
certificate or documentation issued for the purposes of illustrating
compliance to PCI DSS or any other PCI standard are not authorized or
validated, and their use is not acceptable for evidencing compliance.
Also, and I appreciate that this is into the "weeds" of PCI lore, but an assessor is not able to say what "level" a service provider is. The concept of service provider levels is based on brands (i.e. Mastercard and Visa) service provider compliance programs. If the service provider has decided to apply to be on Visa's list, then you can also validate their compliance by looking at the list (although I caution against that because there are some service providers who get one environment or application assessed so they can be on the list but who offer many others that were not assessed) . However, if they say "we are level 2", Visa does not require an on-site assessment (i.e. an audit) of a level 2 service provider, so what you have at best is a self-assessment with some arbitrary "validation" by a QSA. The only evidence of PCI DSS compliance of a third party that shows they have been independently assessed is an "Attestation of Compliance for Onsite Assessments -- Service Providers" - you can see the blank version of this document here:
https://www.pcisecuritystandards.org/documents/PCI-DSS-v3_2_1-AOC-ServiceProviders.docx
So if you have a document that looks like this and which is signed by a valid QSA then you have evidence of the service provider's PCI DSS compliance. Anything else is just optimistic paperwork.