Reddit users analyzed this phenomenon and posted a special post to discuss it. The redditor searched the mobile log to find out why he couldn't see the Gmail message push notification immediately. Their research seems to show that Android "sees" the arrival of Gmail messages, but does not send out notifications.
It has been pointed out that the cause of this problem may be "doze", a power saving function introduced in Android 6.0 marshmallow, which can slow down or disable some functions in Android to prevent excessive battery consumption.
Android authority said that it can't be 100% sure that it is "doze" at present, but "doze" seems to prevent Android system from sending instant push notifications of Gmail until it is pushed by other event triggering mechanisms to "temporarily block" messages. This event may be that the user lights up the screen.
At present, Android authority has contacted Google for information. If there is any result, it will be announced later.