Cannot install macOS on external SSD for 2017 MacBook Pro

The question marked folder indicates no usable OS is found at startup.

If your Mac starts up to a question mark - Apple Support

You'll need to reboot in recovery mode and reinstall macOS on that internal drive, or on an external drive that has been properly formatted. Formatting can be done with Disk Utility while booted in recovery. You must have a good internet connection to the Mac to get this done.

How to reinstall macOS - Apple Support

Your 2012 iMac can run macOS Catalina as can the MBP, so you may be able to use that to create a bootable installer for that OS if you can't get the OS installed on the MBP in recovery. Create a bootable installer for macOS - Apple Support

You cannot create this installer with your 2025 Mac mini.

With Catalina installed on the MBP, you may then upgrade it to macOS Ventura, the newest OS that it can run.

Update macOS on Mac - Apple Support

Edit -

Almost forgot to provide you guidance for installing macOS on your external drive. You can use your 2012 iMac to install Catalina for your MBP.

How to use an external storage device as a Mac startup disk - Apple Support

Since you are not installing macOS onto the internal SSD, then I am assuming the internal SSD has failed. With that assumption, my guess is you are using a non-Touchbar model since the internal SSDs on the 2016-2017 MBPro non-touchbar model had an extremely high rate of failure. I have seen the SSD of a few Touchbar models fail as well, but much less often.

Unfortunately, unless you previously modified the system security settings to allow booting from USB, then you won't be to enable it now without having a valid macOS installed on the internal SSD since you need to be able to authenticate against an admin user account on the internal SSD prior to changing the security settings.

About Startup Security Utility on a Mac with the Apple T2 Security Chip - Apple Support

FYI, it is not worth repairing any of the Intel Macs (especially the USB-C models) for multiple reasons. The money spent on repairs is better put towards a new laptop.

Grant Bennet-Alder wrote:

HWTech is spot-on for MacBook Pro 2018 models and later, which shipped with a T2 chip.

Are you quite certain this is a 2017 model?

Good catch! I was reading a thread about a 2018 laptop just a little while before & just got them mixed up. I would be surprised if this laptop is not one of those non-touchbar 2017 models due to the blinking folder with question mark.

Still good for the OP to check by using the Apple Check Coverage page here to confirm the exact model:

View Coverage - AppleCare & Warranty

HWTech is spot-on for MacBook Pro 2018 models and later, which shipped with a T2 chip.

Are you quite certain this is a 2017 model?