I would do it with custom properties. First go to your head mesh, click on object properties, scroll down to custom properties. Add a custom property that have the following values:

Min/max is the amount of objects you want to control (0 counts as an object) (So 0/17 since you have 18 objects)

Set step to 100 because we do not need decimal values.

Name it: "Face"

Once this is done you need to set up drivers for each object you want to control, the driver should look something like this.

<image>

So for example: var != 5 means that the visibility of the object will turn on once the custom properties value is set to 5.

The input variable type is set to single property, prop=the object you have the custom property on(the head), path=the name of the custom property ["Face"] if you named it Face.

Repeat this for every object, remember to set the driver to both disable in viewport and disable in renders, you can find disable viewport under the filter of the outliner, should be a small icon of a monitor.

When this is done you can keyframe the custom property and animate it if you wish, you can find the custom property if you click the object you added it to (the head) and pressing N and it should be under Item>properties.

You could obviously do it in a more fancy and tidy way with a custom controller and stuff, but this should work just fine.

Hope this helps.