Nick here from Shopify.
Just to confirm, are you asking about being able to fulfill orders automatically and not having to manually do it each time for each order? If so, this is possible natively within Shopify. Shopify has a couple of help guides about this which you can see below:
If this isn't what you mean, can you elaborate a little more on what you're looking to do please!
Thanks for confirming. I'm not 100% sure on api personally, but I will move this topic to the API/SDK board for you and hopefully someone more equipped to answer will see it.
This is an accepted solution.
You should be able to use our Fulfillment API to fulfill a line item (essentially "marking" it as fulfilled). See our docs: https://shopify.dev/docs/admin-api/rest/reference/shipping-and-fulfillment/fulfillment