Sending shipped date when sending fulfillments via API

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I have a program that submits fulfillments to Shopify using the private app API. 
Because of issues with processing large numbers of orders, sometimes we are not able to send the fulfillment within the same day. 
The results is Shopify shows that the order was shipped 1 day later that it actually was. 

My question is; is there a way to send the shipped date when sending fulfillments to Shopify?

I don't see a specific field for this in the fulfillment object and the API doesn't allow setting the created_at field; I tried.