MacPro 2013 No Internal HDD

this is the dark foot-tall cylinder model, right? Not the 2012 42 lb silver tower?

Restart and hold down Command and R keys. The screen should light up offer you some Utilities or a re-install.

How to start up from macOS Recovery - Apple Support

If you truly have no drive, the BIG question is whether it previously ever ran 10.13 High Sierra or later. that would get you the firmware needed to support an aftermarket internal.

The non-obvious other soltion is to connect an external drive, such as a USB drive, and install MacOS on that drive.

if you can get to Recovery, you should get a stable display, and its built-in Disk Utility can tell you about Drives.

Caution: the drive holding or named MacOS Base System of size about 2GB, is pulled for the computer's ROM. It is a disk image, and it is the software that runs Recovery. It has NO space for a new install.

Yes, But...

using that module requires that your Mac Pro 2013 at some time in its life installed MacOS 10.13 High Sierra, so that it got a firmware upgrade that allow third-party internal SSDs to BOOT.

that firmware is stored in a memory on the processor card, so it is not on ay drive, and survives having the drive being removed.

if you can not get a gray screen with some icons in Recovery that Mac may not working properly.

NO drive needs to be present to invoke Recovery. it creates some small RAM disks for it's workspace (sometimes as many as 28).

OWC ( macsales.com) has your back on this one… they offer a 2TB SSD for your MacPro plus install instructions, tools and a few other needed things for $339 plus shipping+ taxes.

John B