Is there a way to use my Apple Pencil (1st generation) with my iPad Pro 12.9 (4th generation)?

Sorry, no. The first generation Apple Pencil is incompatible with the the third/fourth generation iPad Pro.

The 2018/2020 iPad Prom models, with a USB-C port, instead require a second generation Apple Pencil. The pairing and charging method is technically totally different from that of iPad models that feature a Lightning connector.

Here is the full compatibility list for Apple Pencil:

Apple Pencil (2nd generation)

You can use Apple Pencil (2nd generation) with these iPad models: 

• iPad Pro 12.9-inch (3rd generation) and later
• iPad Pro 11-inch (1st generation) and later

Apple Pencil (1st generation)

You can use Apple Pencil (1st generation) with these iPad models:

• iPad Pro 12.9-inch (1st or 2nd generation)
• iPad Pro 10.5-inch
• iPad Pro 9.7-inch
• iPad Air (3rd generation)
• iPad (7th generation)
• iPad (6th generation)
• iPad mini (5th generation)

Not sure which iPad you have? Identify your iPad model.