Can I file an extension on already submitted taxes to allow for HSA excess contribution withdrawal to process?

I e-filed my taxes with Turbo Tax and paid what I owed. I have excess HSA contributions so I put in the option that I would withdraw them before the deadline.

However, my HSA provider now says they might not be able to process the request by the tax deadline on April 15th. Can I file for an extension to give my HSA provider more time to process my excess contribution withdrawal? Or do I just need to hope that they can get it done by the 15th? Do I have any options for how to proceed?