There are a couple of specific criteria in the HDHP / HSA relationship.
You must be enrolled in an HDHP in order to contribute funds to an HSA on a tax preferred basis. You do not need to be enrolled in an HDHP to spend the HSA funds on qualified medical expenses on a tax preferred basis.
One of the qualifiers for an HSA eligible medical expense is the date of service, not the payment date or the billed date. The date of service must be after the HSA is established.
- Along with a host of other qualifiers, I am assuming you have already determined that this treatment is a qualified medical expense and the only outstanding issue is the future dates of service relative to your prepayment date
If this treatment is taking place on 12/27/2018 then you can not pay for it with funds in an HSA established on 1/1/2019. If, however, there will be 2019 treatments paid for by this prepayment, you should be able to reimburse the treatments with dates of service taking place after your HSA is established.
Typically provider offices are aware of navigating these kinds of issues; particularly out-of-network providers that you pay directly. If you tell them what you're doing they can typically arrange things in a manner that's acceptable for HSA reimbursement. One viable solution is that as each specific treatment is rendered the the provider can issue an invoice indicating a billed amount for the specific treatment being applied against your prepayment.