Verbal offer?

Interviewed with a large bank for anAssociate position mid December. Spoke to HR the week after and the recruiter said that they were going to make me an analyst instead with a promotion to associate after 1 year. Then the recruiter went into detail in regards to comp, onboarding process, and set a start date (late Jan.). Was this a verbal offer? I have not received anything written since then although the recruiter said she was going to be out for the rest of the year for the holidays. I called today to ask if there had been any updates but she did not answer the call. Starting to get a bit nervous

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