My old mac has a cracked screen and I can't use it. Is there a way to do migration without doing anything on the old one?

If you have been making backups of this old Mac with Time Machine, you could use Migration Assistant on your new one to restore data from those backups.

Alternately, you may be able to use Target Disk mode, if you don't have backups.

Ref: Transfer files between two Mac computers using target disk mode - Apple Support

Target Disk Mode does not require your Mac to boot up MacOS, because the code to do target disk mode is all in ROM.

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In addition to the above suggestions, you could connect an external display or TV set.

Although you may need an adapter, no additional configuration should be required.

If you see only wallpaper, Command-BrightnessDown toggles the sense of [√] Mirror displays, to make the external display show the same images as the built-in, if not already.