Hey!!
This issue is generally easy to fix. Here's a few ways!
First - check that you're signed into the App Store services on your iCloud. To check, open Settings, click your name, and click "Media and Purchases". If there is a "sign out" button, try signing out and back in again.
Next method: Navigate through Settings to the "Music" tab. I'm not too smart with iPad, and I saw you said the "Sync Library" option isn't there. See if it is, if not, try the next method.
Final method: If you use a Mac laptop/desktop, or a Windows PC, open up Music (Or iTunes, respectively), click "Songs", click one and do CMD (or CTRL)+A to select all songs. Right click and click "Add to iCloud Music Library" and let it sit for a few minutes to upload and sync those songs to Apple Music.
Best of luck!