UCC28740: soft start design

UCC28740 soft start is embedded inside the IC in terms of pulse width from narrow to wide and in terms of time. If further output voltage slope needed, you can add some more output capacitor to slow down or to reduce some output capacitor to accelerate output.

Another thing you can do is to make Iocc bigger to accelerate output which is equivalent to increase output capacitance, if a bigger Iocc is ok. A smaller Iocc can make turn on slower if you can accept smaller Iocc.