I'm assuming the computer is "locked" but online, and no users consent to logging in to run anything. Will any of these methods still work if Firewire drivers are disabled?
In that case USB-C/Thunderbolt won't work, in the default config you need to trust the device and cable before anything too interesting can happen. This can be turned off via bios setting though, so there's room for misconfiguration.
E-SATA or PCIe hotplug might still work. However the former is getting less common, and the latter is uncommon in consumer mainboards.
E-SATA or PCIe hotplug might still work. However the former is getting less common, and the latter is uncommon in consumer mainboards.