Hi Ryusuke,
While there is no fixed recommended value here - the max value will be bounded by the loop response and as you mentioned - the current limit. The device has internal soft start and hiccup mode to deal with this inrush.
Based on your specs…
Part Number: TLVM13660 I am designing a PDN based on the TLVM13660. On the TI website, I found a page referring to a calculation tool ( https://www.ti.com/tool/TLVM136X0DESIGN-CALC), but on that page I cannot find a reference to the actual software. …