How to upgrade boot rom firmware without an original drive

I have a 2015 MacBook pro that I am in the process of refurbishing. I purchased it used and it was missing many parts (wifi card, IO board, SSD). I have replaced all of these parts and purchased an aftermarket SSD (it looks like an M.2 with an adapter on it).

The machines internet recovery wants to install Yosemite so I assume this machine is on an older firmware version which predates support for NVME drives.

As far as I understand I need a boot rom upgrade that comes with high sierra in order to boot/use the aftermarket disk. I tried installing Mac OS on an external disk and upgrading it to High Sierra, but I ran into a firmware validation error.

Since apples boot rom/EFI firmware upgrades are staged on the internal disk, it seems this upgrade path is impossible without an original proprietary apple drive.

Is there a way to manually install the boot rom/EFI firmware upgrade in this situation? or is my only option to purchase (a very expensive) original apple drive?

Update: I have personally resolved this by sourcing an original drive, running the upgrade, then swapping in the new drive. I will accept an answer to this question if a feasible alternative is proposed.

Why not try the (alternate) command and (better) restore using latest macOS?

https://support.apple.com/en-us/HT204904