Luckily, Android has a software management system that doesn't rely on the Playstore. You can download what are called APKs and install those instead of using the Playstore. It should be stressed that the Playstore should be the only place where users should download software from, and that the method listed below is only in emergency situations where for whatever reason, the user is unable to download via the Playstore.
Go to the settings app and press the "Security" tab.
There will be an option titled "Unknown Sources" or something similar to that. Tap that option.
A message will pop up, asking you if you want to allow the device to install software from unknown sources, tap yes.
Go to apkmirror.com on the tablet or device and search for the Google Play Store.
Find the most recent version that doesn't have "Android TV" or "Android Wear" in parentheses next to it.
Tap the arrow to the right of that version.
Scroll down at the new page you are on until you see the "Download" header.
You will see a variant, at the time of this writing it is 7.8.15.P-all. Ensure that it has  and not  or .
An ad will pop up. Press the "Close Ad" square.
You will be at a new page, scroll down until you see the box that says "Download APK".
Press that box.
You will be taken to another page that says your download has started.
You may get a pop up box that asks if you are sure you want to download the APK. Press "OK".
You will see at the top of the screen a little arrow appear which will signify the download has started.
When you see that arrow turn into a check mark, open up your file manager. This app will be called either "My Files", "File Manager", or "Files".
Scroll down until you see a folder that is titled "Download".
Tap it to open the folder.
Scroll until you see the name of the APK that was just downloaded, in the case of this writing, it is 7.8.18.P-all.
The process of installation will start.