The Cainiao website provides an estimated delivery date both on the web site and in the API.
https://global.cainiao.com/global/detail.json?mailNos=*removed*&lang=en-US&language=en-US
Gives an json message and module[0].globalEtaInfo.deliveryMinTime and module[0].globalEtaInfo.deliveryMaxTime give a bound for for the delivery time in miliseconds since the Epoch. In all examples I have seen they have the same value.