Some questions about the CN3722 solar charging IC and its MPPT setting
Why doesn't a charging cycle begin, when the MPP voltage isn't reached?

Best guess: A solar panel is a current source over most of its characteristic; the output voltage is set by the input impedance of whatever charger is connected to it. MPPT in this IC probably works by reducing the current it delivers on the output until the MPP is reached. If it can't reduce the current enough to get to the MPP by changing its input impedance, then there isn't enough current for charging.

How can I obtain its MPP voltage?

Oversimplified, but good enough, probably: You could measure the open voltage and shorted current of the panel under full sun, giving you two points on its I/V characteristic curve. Then draw in a characteristic with the same shape (not values) as done here:

(Image source - my website: Using a solar panel for USB charging)
You can then make an educated guess of the MPP from the curve; the surface of the rectangle should be roughly the 1W mentioned in the spec of the panel. Note that in the image, the open voltage is 21 V and the shorted current is 0.62A; not the values you will see.
Alternatively, you could do more complex measurements, or you could mail the supplier and ask for more specs 8-).