There are a number of ways you might approach creating a zoom in from a view of the planet. To start off, you can use Adobe After Effects: this will be the option that gives you the most control of what your final outcome will look like.
But, like most things, it will exchange control for labor intensity. While it isn't difficult, you'll be faced with an abundance of options throughout the process of making your video.
Your second option is a combination of the Google Earth desktop app, a screen recorder, and a little bit of touching up in the editing software of your choice. This will be very simple, fairly quick, but might not be the best possible quality, as you'll need to crop out all the excess information in Google Earth's heads-up display.
This video will walk you through the steps, but since the person making the tutorial is using an iPad, you'll need to swap LumaFusion with an editing software of your choice.
This is the final, and likely your best choice, but with one caveat: you'll have to apply for access to it. To my understanding, access is granted on a case by case basis at the moment, as it is still in a pre-release stage, but usually they will approve access within 2-3 days.
Creating zoom ins is exactly what this program is created for and will give the easiest access, best quality, and likely the most possibly control.