termite damage showed up 3 months after passed inspection, is this possible?

My husband and I got a termite inspection done in December, it passed, so we bought the house. In March we noticed a whole in the wall with termites coming out of it and drywall damage which indicated mud trails. We called a different company which confirmed that we had termites and got the treatment done. I read in many places that it can take years for termites do do noticeable damage. So is it possible that there were no termites in December if 3 months later there is damage? Can the company that originally passed the inspection be held liable for damages?

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