Can an OpAmp be built without an IC or transistor or a Vacuum tube?
Opamps have power gain, so one way or another you need a external power source and active components.  You have ruled out the usual active components used for amplification in electronics, which are transistors and vacuum tubes.

You therefore need to get clever and find other ways to amplify.  That means you need to be able to control a large amount of power by variations of a small amount of power.  Some possibilities:

A motor driving a rheostat.

LEDs controlling LDRs (light dependent resistors).

Pressure-controlled water flow valves.

Pressure-controlled pneumatic valves.

A gasoline engine with the control being the throttle.

A mechanically controlled adjustable transformer, like a variac.

A electrical generator where the power input is the mechanical rotation of the shaft, and the control is done by changing the field winding current.



Once you have something that can amplify, you still have to use it, or several of them in the right configuration, to make a opamp.  This is just like a transistor isn't a opamp, but multiple transistors arranged the right way (with some passive parts) can be a opamp.