Switching power supply delays delivering power
Yes, power suppplies need a little to time to stabilize its output voltage after turn on. Some need a minimum load to work fine. It depends on the specific powersupply. Try looking at the supply documentation to see if that is the case. You should try adding the delay you mention in the question to see if it improves.

Another thing to consider is that motors generally draw a big amount of current at start transient. If possible add a soft start to the motor, so it gradually increases its speed.