Indeed, you are likely missing an essential adapter…
As you are evidently aware, the first generation Pencil is charged and paired from iPad10 using the iPad charging cable - and an Apple USB-C to Apple Pencil Adapter:
New first generation Pencils now ship with this special adapter in the box along with the Pencil. However, some older stock purchased from retailers may lack the USB-C to Lightning adapter - and may instead have an older Lightning to Lightning Adapter.
For owners of older first generation Pencils, or for “old stock” new Pencils, the new special adapter can be purchased directly from Apple as an accessory.
https://store.apple.com/uk/xc/product/MQLU3ZM/A
As such, if purchasing a new first generation Apple Pencil to accompany an iPad10, you might be best advised to visit an Apple Store or Apple Authorised Retailer that has a high-turnover of stock - and ensure that the Pencil box indicates that the correct adapter is included.
If necessary, open the box in the Store and check that the USB-C/Lightning adapter is present - noting that the older Lightning/Lightning adapter looks very similar to the USB-C/Lightning adapter.