How long does it take for products to be published to a sales channel after it is installed?

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I'm building a sales channel and noticed that there's some lag between a merchant installing our app and their products actually becoming published to our sales channel.

Does anyone know how long this process typically takes? Is it reasonable to expect that Shopify will finish the process of publishing products to a newly installed sales channel within a certain time frame like 15 minutes or 1 hour? If not, is there a way to know when Shopify has completed that process of publication?