Welcome to the community, @Justin_Weddle !
However, for an easy no-code way of accessing Dropbox’s API (or any other cloud service provider’s API), you could simply use Integromat to achieve the same affect.
Of course, once your files are cloud-based, you could always just store their URL in Airtable, and then click on the URL in Airtable to open the file from the cloud service provider. This might also be your best option, because Airtable has a relatively low size limit for attachments in a base.
p.s. Note that I am a professional Airtable consultant and a Registered Integromat Partner, and the Integromat link contains my personal referral code. If you have a budget for this project and you’d like to go down the Integromat path, you can certainly hire me to help you with this! Feel free to contact me through my website at ScottWorld.com.