My wife and I are currently in the process of getting her a SSN but do not have one yet, and likely wont prior to 15July. Should we apply for the ITIN in the meantime?

She received her greencard in April, but for some reason did not get the SSN when we checked that one was needed. We are having to reapply for it, so my questions is, in order to file taxes on time, should we apply for an ITIN in the meantime? It says to be eligible for an ITIN, you should not be eligible for a SSN, so I am not sure if it is even an option? Any help would be greatly appreciated.