One process to do this is outlined in this government document.
This document basically instructs you to trust the issuer of this signature on the local machine by importing the issuers certificate in the document into the local trust store. It is local only, i.e. it only makes changes to the local machine and not the document itself and thus these steps need to be retaken on any other machine were the signature should be checked.
If these instructions are all what you get, then I find this very questionable. The point of validating a document signature is to check that the document is issued by the expected person - so there need to be some expectation already. Since you don't know the issuer and signer of the document personally there is usually some trust chain involved to get to this expectation, i.e. you don't know the person directly but you trust the government (in this case) and the government cryptographically tells you that they trust this person (as government employee). See chain of trust for a deeper explanation of this concept.
What you are asked to do in the instructions is different though. There is no mentioning of a trust chain (even if there is one shown on page 3) but instead you are expected to simply trust the person because the instructions tell you to trust them. Blindly following these instructions will also make you trust non-government persons, i.e. potential scammers. Adobe even kind of warns you against doing thus, but unfortunately only in a technical terminology useless for most users (page 4):

Additionally these instructs ask you to grant very broad permissions, specifically to make the certificate associated with the document a trusted root. I'm pretty sure that this is not needed and could in fact be harmful. In fact, it specifically says that in this case it will not be checked if the certificate gets revoked, which might happen if the government removes the trust from this employees certificate (like certificate compromised, employee left, ...). Unfortunately again only in technical terms (page 5):

In other words, these instructions are not intended to actually provide security. They are only intended to somehow show the green tick mark. My hope is that the person who ultimately needs to get these documents will do some proper checking, your task here is basically only to weed out early problems before uploading.