Hi @mshah72 !
I do not think it is possible out of the box, but certainly is possible.
Adobe Sign has an API so it
https://secure.na1.adobesign.com/public/docs/restapi/v6
Which seems to be having option to upload a file and specify recipients:
https://secure.na1.adobesign.com/public/docs/restapi/v6#!/agreements/createAgreement
Meaning it could be created pushing data from Airtable via Automation to Adobe (* however I did not check authentication format.
I see that you can also use Make.com and they have the "Create an Agreement" module:
I have not used the Adobe API, so it would require some time dig through docs and test, but you could try to see if it can work out yourself in Make.
If you would be interested to use DocuSign - I have somewhere implementation instructions. Cannot tell though if Adobe or DocuSign would be better for your use case.
I hope this helps!