However, the component has a large capacitor that causes an initial surge of current. This prevents the regulator from coming up, although I am not sure why. If I power up the regulator first and then connect the component to the regulator output it handles the initial surge of current and maintains the 5V output.
Is there a fix for this startup problem or another 5V Step-Up Voltage Regulator that would work for my situation?
Could you tell me more about your load (e.g. what it is, the capacitance, the current draw, etc)? It sounds like you are using a LiPo to power the regulator. Is it fully charged?
Is the 0.47uF value you stated correct? That is not normally considered a large capacitance (it is not unusual for some electronics to have capacitors in the hundreds of microfarads), but I could see it still representing a significant load if it is on the high voltage side of that module. Have you tried monitoring the input voltage to the U1V10F5 to make sure your LiPo is able to supply enough power while the HV board is starting up?
That 700 - 1000V regulator is a pretty special load and it is not surprising to me that it would have a very large inrush current or that it might cause issues for the U1V10F5. If that is the issue, you could try one of our higher power step-up regulators like the U3V70F5. Since it can handle a few amps of current, it is much less likely to have trouble starting up.