Suppressing Transient Voltages - DC circuit
You really need to take a look at the inputs using an oscilloscope to see if the issue is that you are exceeding the absolute maximum input voltage for the switching converter, or if it is some kind of switching startup issue.

If the problem is high voltage (or high differential voltage caused by ground bounce):

It is possible that adding a relatively high ESR electrolytic capacitor on the input side might help with the inductive spikes on the input.

It is also possible that using input protection (probably a unidirectional TVS diode) will solve the problem.

If the problem is a switching startup issue:

Most switching converters have a slow-start circuit, usually an internal current source that charges an external capacitor.  This is used to limit the startup current required to charge the output capacitors on the switching converter and at the load.  Increasing the value of this capacitor (slowing the startup) can solve these kinds of issues.