Did they actually hire me?

I don’t know if you guys can help me, but I recently got hired by a company and they told me I would receive the offer letter by end of day Tuesday, it has been few days now I called on Thursday to follow up and I was told it will be sent. I called again today to follow up and they said it was sent out yesterday, but I didn’t receive anything. I asked for it can be resent if possible they said they’ll do that still haven’t gotten anything. I even provided an alternative email address and I still haven’t received anything. I’ve even checked my junk mail on both emails. What should I do?