If you have no schematic, the controller IC typically is a chip with approx. 20 leads, with a small bunch of small SMD passives (resistors and capacitors) around it. One of the leads goes to a small capacitor, other end of which goes to ground. If you measure the voltage at this capacitor during operation, it should be at least the reference voltage of the IC (typically 0.8V to 1.2V), or more in some ICs, but definitely no less. If you have an oscillosscope, you should see a stable DC voltage; even better, scope it during turn-on, and you should see it ramp from zero, during a few milliseconds. This is your softstart capacitor and you can try replacing it with a larger value like 1uF and see if the output ramps more slowly during power-up.
Remember to be very careful when probing or modifying mains stuff, see the usual advice elsewhere.