LM3478 48V boost converter
Not a full answer, but...

You probably have to delay its startup.

Why? 

If the input supply is initially at less than the full 24V, a boost converter will attempt to generate the full output voltage by drawing excessive current from it.  ( P = I * V ... lower V implies higher I for the rated power) That will trigger whatever protection the input supply has, preventing it increasing its output voltage, and (depending on the supply circuitry, holding it in "foldback" at very low voltage.

With the power supply running first, it already supplies 24V when the boost converter starts, removing the need for excessive current at low voltage. The same is likely true if COUT is already charged close to rated voltage.

Delay the startup, and the boost converter should stay within the supply's rated current. (There will be some surge as it charges Cout but your results suggest the PSU can cope with that.)

How?

Look for "inhibit" or "power down" or "standby" hints in the datasheet. You didn't link it so I'll leave that as an exercise. I can't see an "inhibit" pin in your schematic but there are sometimes documented ways to use the "FB" or "comp" or "Isense" pins for the purpose..

Then apply appropriate signals to those pins for an appropriate time after startup. Test thoroughly; switching off and back on immediately can catch out some of these strategies.