Single or family plan? If single, you won't even have the full $4k yet, so it's out-of-pocket anyway.
Also, make certain your dental work is medically necessary, not just cosmetic. Cosmetic procedures like veneers, whitening, straightening, etc. can't use HSA funds.
Otherwise, if you have the funds to pay out of pocket, do that and save a digital, cloud-based copy of the receipt. If you have financial trouble in the future you can redeem the amount on your receipt. You can even redeem it in 30 years for that original receipt amount.