You can use the EPA (before the donor loses mental capacity to act) at any time, as long as you have the donor's permission. So all you and the donor will need to do is to check on the bank's requirements for proving that such permission has been granted. They might, for example, simply accept a signed letter from the donor but they could equally insist upon further proof of permission (such as you presenting the donor's passport or other ID document). So start by contacting the bank.
That's actually no different to the situation where no EPA (or LPA) exists at all. Anyone can authorise someone else to carry out financial transactions on their behalf.