When does my eSIM data plan start?

Your eSIM data plan starts when you activate it on your phone, not when you buy it or when you install it. It means that the eSIM plan will not activate when you scan the QR code. After scanning the QR code, your eSIM profile will be downdloaded and you will take some on-screen steps to activate it like switching on data roaming. This is when your plan starts counting down.
If you do not activate your eSIM, your eSIM plan will not start and you will still remain the whole length of your plan. Then you can activate it later after arrival in your destination.

When should you activate your eSIM plan?

It is advised to activate your eSIM just one day before departure date or even on the same day you start your trip when you can access to the Internet. This helps you avoid losing any days of connection.

Should I only buy an eSIM when I am ready to use it?

No, you can buy an eSIM plan whenever you want.
For example, assume that you are going to travel Thaialnd from 1st to 10th May. If you buy a 10-day Thailand eSIM and activate your plan on the 1st May, it will last for your whole trip. But if you activate it on the 30th April, the plan will not cover your entire trip.
But if you buy a 10-day Thailand eSIM and your trip only last 5 days, you can set up your eSIM a few days before departure. Just make sure that you are connected to a stable wireless internet when installing and activating the eSIM.