I just purchased Mathematica 12.3.1 Home Edition. I'm running it on a Microsoft Surface Book with Windows 10.
When I start Mathematica and enter a simple calculation, e.g., 2+2, it takes between 3-5 minutes for the kernel to initiate. After the kernel is initiated subsequent calculations are extremely fast.
Why is the kernel initiation so slow and what can I do to speed this up? Is there a logfile that I can read to understand? This is a very annoying issue.
How much memory do you have and what else is running on your laptop? Quit Mathematica, start task manager, start Mathematica, do a simple calculation and monitor memory / cpu in task manager. That might help to identify the issue.
You can evaluate this to see where time is being spent during kernel startup
FE`Evaluate[FEPrivate`$StartTimes] // Column