Technically, you can only launch a site through the API.
The problem you may encounter is practical, instead of spending time learning all the API calls, you can learn how to implement your current interface in Magento.
The advantage of this approach is that you will also better understand how Magento works internally, which allows you to use its functionality for your unique business needs.
Another problem is that when using the API you have a little less control over how things are processed / calculated, and when working in Magento there is a lot of control over the specifics.
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