"Royal Mail International Signed For" service uses GLS to ship across Europe to Athens and then ACS for delivery within Greece. If you put the Royal Mail number into the GLS tracking web site, https://gls-group.eu/EU/en/home
it will tell you both the GLS tracking number and the ACS number. You can use the GLS number to track progress across Europe although it isn't very detailed. The ACS number will not work until the package has been handed over to ACS in Athens https://www.acscourier.net/en
Make yourself known to your local ACS office and you shouldn't have a problem. Typically they will only phone mobile numbers.
Incidentally the last two packages I had delivered from Amazon were shipped by Asendia, a company I have never heard of before, with no tracking information. I contacted Asendia and asked who they used to complete delivery in Greece. They said that they didn't know but it was probably the post office. I must admit this did not inspire confidence but they were both delivered by ELTA about a week later than predicted.