I would need a date/time picker in order for user to choose date or time in google hangout chat bots.I could not found any documentation on this function in google hangout api.
Example:
staff wants to apply a leave for few days. She/he can do it by just selecting date or time in calendar.
It's not currently supported, no. https://developers.google.com/chat/api/reference/rest/v1/cards#datetimepicker