I don't have this device and just want to share this method. Use it at your own risk!
BBB100-4, upgrade to AAO472 or newer, Android 7.1.1
1. Download GMSV4.1.apk from link above, copy it to phone and install
(1) You will see a new app called “谷歌安装器-水星版”
(2) Make sure you did not install any other GMS apk before!!!
2. Enable GMS
(1) Open the app you just installed and click the button, “开启GMS” as shown below. There would be a pop up saying “开启GMS”. After a few seconds, the pop up will close itself.
(2) Enter System Setting, enter Developer Options (*), find “Enable GMS” at the bottom. After you switch it on, you MUST reboot your phone.
*How to enable “Developer Options”: enter Settings-About Phone, click “Build Number” 7 times.
3. Set up location permission for GMS services.
(1) Enter Applications-Options (Gear Icon)-Permissions-Location
(2) From right corner 3 dot menu, “Show system app”, grant permission to Google Play Store, Google Play Service, and LocationServices.
4. Set up GMS apps permissions
(1) Settings-Application-right corner 3 dot menu, “Show system”
(2) Find out all GMS applications (including Google Backup, Google Calendar Sync, Google One Time inti, Google Play service, Google Play Store, Google Service Framework, Google Partner Settings, Google Contacts Sync, Google Account Management. Click them one by one, then click Permissions and grant all. Make sure you grant all permissions on all Google apps!