Why can't I access the App Store on my Apple TV?

I’m not sure in detail of what you are experiencing, as it should be the same for anyone with Apple TV HD (4th generation) or later models, with an Apple Account set to a country where Apple offers the App Store on Apple TV hardware (same countries as where Apple sells the Apple TV box). It works as intended on my unit.

1. Find the App Store app on the Home Screen.
2. Open the App Store app.
3. Notice the ‘pages’ within the app, as indicated with ‘tabs’ along the top of the screen: Discover, Apps, Games, Arcade, Purchased, Search. Navigate to Search (magnification glass icon) if you know the name of the app that you want to install. You can type the app name there. (More generic keywords are also supported in Search.)

If the App Store app seems to misbehave, then:

1. Force-quit the app, then relaunch and try again.
2. If the issue persists, force-quit the app, restart the device, then relaunch and try again.
3. If the issue still persists after that, then contact Apple for further assistance.

Note that the App Store on the Apple TV box has compatible apps only. This may differ somewhat from the App Store on iPhone or iPad. App developers can choose to program for specific devices, and release their app on App Stores on those devices only.

Aside from that, there is also a regional availability option. Apps can be for a specific set of countries and country-like regions, as their developers see fit.

I changed my settings so that date and time updated automatically and that fixed the problem.

Excellent! Enjoy your App Store access again.

If the date/time/timezone is significantly off, then that may cause issues with secure connections that require a time stamp that is somewhat accurate. That may have caused your issue, from what I can assess. And Apple will use secure connections for just about anything that they send or receive electronically, including accessing an App Store.