could it be that what you mean by
using Game SDK
is that you went to the marketplace, bought it there and afterwards it showed up in the 'My Assets'-page in the CryEngine-Launcher and you downloaded it?
Having the GameSDK downloaded doens't mean that all the assets will now show up in the editor. To access the GameSDK-content, you need to import the GameSDK-project. To do so follow these steps:
1. Go to the 'My Assets'-page
2. Click on the dropdown-menu of the GameSDK which shows 'Installed', click on 'Reveal in Explorer' (now the GameSDK-location opens in a separate window)
3. Go to the main-page of the CryEngine-Launcher and click on the 'Import'-button
4. Navigate to the location of the downloaded GameSDK (e.g. C:\Program Files (x86)\Crytek\CRYENGINE Launcher\Crytek\gamesdk_5.3) - it is important that you select the GameSDK-folder which is located inside the gamesdk_5.3-folder and click 'Ok'
5. Now the project shows up in your lists of projects with the name CRYENGINE SDK
6. Click on it to launch it in the editor or click on the gamepad-symbol to launch it in GameLauncher.exe
When the GameSDK-project is opened in the editor, you can create a new level from there using all the assets provided within the GameSDK. You should then also be able to export your level and start it in GameLauncher.exe.
I hope this fixes your issues. Cheers