You can still use a zener diode to create a voltage that is lower than the lowest possible supply voltage. And then scale your input voltage accordingly. This way you will be independent from the actual power supply voltage, as long as it is high enough for all the ICs to remain in spec.
I would be looking to use the solar panel as my SOLE power source.
So when it's dark it's at 0v and the circuit is off.
Then as it starts to lighten up (sun coming up or on cloudy days): it would be say 1-2v which would not be enough to turn on my arduino and accompanying circuit.
Then as it gets sunny and goes to say 3.3v+ I'd like to turn it on. I have some cheap buck boost converters I could use to maintain the 5v but that might be overkill/a waste/too much load.
Then as clouds pass over or it gets dark it could turn off if drops below 3v and not come back on again till 3.3v to prevent rapid cycling.