Push products to printful syc store from Shopify API

Hi,
I’m having trouble pushing products to my Shopify Sync store. I’ve manually created and synced products between my Shopify store and Printful store. However, I’m unable to create a product on my Printful Sync store via API because Printful doesn’t allow this for Sync stores. So, I tried creating a product on my Shopify store using the Shopify API, but it’s not pushing the product to my Printful store. Essentially, the product I created using the Shopify API isn’t showing up on my Printful store, which is linked to my Shopify Sync store.
Any of the members had similar scenario ?