You handle that BEFORE installing the new drive.
You need to CLONE, not copy, the old drive the the new one before removing the old one from the computer. That is how I transferred everything from the old HDD to an SSD on my 2012 Macbook Pro.
Get an inexpensive USB3 empty drive enclosure like this: https://eshop.macsales.com/item/OWC/ES2.5BU3B/ to be a transfer enclosure. Makes this SO much easier!
I recommend Carbon Copy Cloner (CCC) because it prompts you to recreate the important Recovery partition on the new drive.
Connect the transfer enclosure to the Mini and use Disk Utility to format the SSD. Use CCC to clone the old drive to the new. Once things are transferred and you confirm that the new SSD is bootable in the enclosure, only then do you move the SSD to its new internal home.