How do I switch on after the current (out of a power supply) has established?
Your PS3X-C12AFC 12v supply is a FAR more stable source than a car battery. And its turn-on transient is well controlled. This moves attention down-stream to the USB charger, and R-Pi requirements and characteristics. Any turn-on transient created by the USB charger should never over-volt your R-Pi. I would hope that a USB charger is properly designed to not over-volt (they would very soon get complaints of blown USB appliances). And the USB charger should also cope with zero-to-full current as you plug a device into it. That said, many clone-makers of these "chargers" make it a weak-link in your power-supply chain.
The turn-on sequence that you describe (plugging the USB + R-Pi into a previously powered-up PS3X-C12) seems to work for you. Leaving everything connected, and plugging the PS3X-C12 into the wall should work fine. A "power-good" circuit is not required.
By-the-way, it is impossible to monitor current before applying power.