Hi.
I tested one of those U1V10F5 regulators with a 100ohm resistor here and was able to get a similar result by current limiting my supply, though I had to use a somewhat lower limit of about 600-800mA to get it to reliably happen. When that regulator starts it draws a quick burst of current, and if the power supply limits that, the regulator never gets a chance to fully turn on. Here is a scope capture of the input current of the regulator at turn on with a 100ohm load and 5V input:
If you are able to increase the current limit of your supply to 2A, could you try that and see if it works? Could you also try a different power source like a battery?
-Claire