It does make more sense that he departed around 7 am and the friend noticed him overdue after about noon. And it also makes sense that he sent GF the trailhead photo when he had cell reception near Asphonidilatus, rather than when he actually departed.
The important detail we don't have is the TIME that Sophia Liviaki sold him the soda and the water presumably at Asphondilatus .No article I can yet find specifies the time or location other than "two hours after he left".
Did she see him around 9 am or 11 am?
The one paragraph that I can find that mentions her, from a BBC news report:
About two hours later, a local woman said she spoke to the missing tourist after he bought drinks from a nearby store. Sofia Liviaki told Mega TV that Mr Calibet had drunk a soft drink, showed her his planned route and took a bottle of water with him for the remainder of his journey.
Local officials say the 59-year-old did not return after setting out on a hike on Tuesday.
www.bbc.com
*Edited to add source