How to verify if power supply is enough to handle power consumption spike?
Yes find a higher power supply. Peak power is intended for the spike when you turn on the device.

Most circuits and especially those with electromechanical components such as disk drives, motors, fans, actuators and pumps, requires start-up currents that are usually higher than the steady current that the equipment draws when operating normally.

https://www.sunpower-uk.com/glossary/what-is-peak-power/