Your illustrated USB-C to Apple Pencil Adapter is the adapter that you require. You need to ensure that the long Lightning connector, beneath the cap of the first generation Pencil, is fully engaged by pushing the connector all the way into the Adapter’s Lightning socket.

When properly inserted, there should not be a gap between the Adapter and Pencil.
If you are still having difficulty, you would be best advised to visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to assess your iPad, Pencil, Adapter and cable:
Genius Bar Reservation and Apple Support Options - Apple