After you fetch the product data from the original store, you can use the REST Admin API or the GraphQL API to POST that data to your Shopify store. If you are hoping that Shopify's APIs will have a way to fetch data directly from your original store? You might be out of luck, but I won't say definitively. I simply don't know of a way to implement such a process.
Shopify Docs: https://shopify.dev/docs