Earlier quoted context omitted.
Not all employers offer HSAs to go along with their HDHPs. Mine doesn’t and it’s very frustrating. I want to save pretax money in an HSA but I can’t.
There is no requirement for your employer to provide the HSA. Frequently the employer can get better deals on the HSA than you can individually (like no waived maintenance fees and the like) but you can for sure open your own. In fact once you have enough money in there that you are moving out of liquid investments then you definitely want to shop around for HSA much like you would for an investment account.
(FWIW, I have an HDHP, employer HSA, and an individual HSA that I roll my employer funds to annually for lower-fee investing.)