Update your post to include full system hardware specs and OS information.
Make and model monitor?
Is it the computer that you turn on and off and on again? Or is it the monitor?
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My thought is a loose connection or component somewhere. Needs to warm up, expand, and thus full connectivity.
Have you tried another known working DP cable?
If you swap in another known working monitor with displayport does the problem remain?
Does the current monitor work using displayport on another computer?
Objective is to discover if the problem follows the monitor or stays with the computer.