In my process i have two reasons not to put my start interface in the properties in (process start from):
first because i have to check condition before start the interface
second because the cycle contains loop and i can't loop to the start node
The Process Model works well in the debugging but it can't be added to site or initiated from Action button
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The main disconnect here, in case it wasn't clear, is that you can't define a process model as a Site Page unless it has a start form.
In your case, I'd suggest just using an interface for that site page, and allow the user to click a Start Process Link to begin the process model, in which case you can perform the checking in the initial XOR gateway and route them to the correct task. You will need to enable chaining and correct the flow directionality from between the upper task node and the XOR, before it will work correctly.