Using the HDMI out on the phone is the best option. If your phone doesn't support video out, this is the best way I found to do it.

I recently had to do this with my pixel when the screen died. I couldn't find this advice anywhere so I'm super proud of this work around. Unfortunately it's not easy. You'll need a OTG adapter, a wired keyboard, a Bluetooth keyboard, and a crap ton of patience.

Step one: enable android talk back/screen reader. This can be done using the volume keys or Google assistant. https://www.theverge.com/23184596/android-screen-reader-how-to-enable

Step two: connect the wired keyboard using the OTG adapter. Use the keyboard's keys to unlock the phone and use the arrow keys to navigate to the Bluetooth settings.

Step three: connect the Bluetooth keyboard to free up the USB port on the phone.

Step 4: use the Bluetooth keyboard to enable the backup method of your choice.

Bonus advice: Use Google play store on a computer to remote install a screen cast app https://www.howtogeek.com/690556/how-to-wirelessly-mirror-your-android-phone-to-your-tv/

Use the wired keyboard and screen reader to open the app and start the screen cast. That makes things much easier.

You'll need an OTG MHL adapter that has HDMI out as well as USB for your mouse.

Hook up to a TV, and it should just work..

The touch layer may still work. If so, you can plug it into an external display and poke around not completely blindly.

Yes! If you replace the broken screen with a working one, you'll be able to see the interface, and then you can enable USB file transfer as you would normally.

As other people said an MHL cable might work - if you had the debug setting to allow MHL cables to display to an external monitor

If you did not enable that setting your only option is repairing the screen

Good luck!