Most newer PSUs, of good quality, has a low power mode, basically unless the PSU hits a certain load the fan will not start to spin. If you just power it on without any load, a power on test, it will not spin.
For example, my Corsair AX860is fan will not start spinning until it gets to higher than 20% load so 172w which is well more than my system at idle or even low use.
Which PSU do you have?