I would use the combination of Integromat and PDFFiller to do this for you.
You would click on a button in Airtable, and it would automatically fill out all the fields on the PDF form for you, and then it would add the filled out form as an attachment to your record in Airtable. It could also email the form or do whatever you want with it.
p.s. If you have a budget for this project and you’d like to hire an expert Airtable consultant & Integromat Partner to help you create this, please feel free to contact me through my website at ScottWorld.com.