First, did you use any money from your HSA in 2019? That is, did you spend any HSA money (usually with a debit card) on qualified medical expenses in 2019?
If you did not, then they won't send you a 1099-SA, and that's OK because you do';t need to enter in this case anyway.
Second, if you did spend money from your HSA in 2019, did you look online at the HSA custodian's website? I believe that many HSA custodians provide copies of your forms online (mine does).
Third, nobody sends you a 8889 - TurboTax fills it out for you based on your entries, and adds it to your return.
So, did you spend any money from your HSA in 2019?
There is a clear misunderstanding here. If you spent money (made a withdrawal) from an HSA (health savings account), the administrator MUST issue a 1099-SA. I doubt that any legitimate bank would refuse to provide one.
If you have an HSA and made withdrawals, call again or check your account on their web site. You may be able to download the 1099-SA. You do not get a 1099-SA if you only made contributions and no withdrawals.
If you have an FSA (flexible spending account, from a work cafeteria plan), then you don't get a 1099-SA and don't report it on your return. An FSA is not the same as an HSA.