start up circuit
It requires start-up circuit for sure.
Why cant the opamp output be at VCC when both inputs at ground? To test it, you need to initialize all the nodes such that there is zero current in the loop and run the sim at slow & cold case. Then add offsets to see if it works. In these circuits, most of the times it is the fast supply ramp that prevents it from working. A monte-carlo sim can also be run to show the need for startup.
At low currents, the re (1/gm) will be much higher than the dVbe resistor, so there will be little to choose between positive and negative feedback, a small offset is enough to see the positive feedback reign.