Greetings from Turkiye, my neighbor
By saying Turkiye, you may have noticed that I am writing from a place where olive or olive oil is not needed, but I want to write a few things.
First of all as we know, the olives grown in Greece and Turkey are of very high quality due to the climate. That's why it has huge demand from all over the world. In order to keep up with this demand, serious work and agreements have to be made. And also it requires high capital.
Within this work, there are parts such as packaging, storage and transportation that create serious costs and labor. However, I would like to talk about a method made in Turkiye. Maybe you are already trying this method.
I know that cruise ships come to the island of Crete. Each ship has a minimum of 1000 people and it goes up to 5000 people and these people usually come from America. Here you can organize tasting tours for them; you can organize a workshop where they can try gather the olive from the tree to the olive oil stage. You can also include dishes that are unique to the island of Crete and made with olive oil in this workshop.
I don't know what the legal sanctions are on this island, but you can open an account on Tripadvisor and put it as a tour, or you can contact the tourism agencies selling tours in there and provide such a service and deliver your olives to consumers faster and at a lower cost.
I would like to add something to the question you asked in the subject. Many countries have different procedures for imports. Some are very costly and some have very strict requirements. At this point, my humble advice is to focus on certain countries to start with. 4-5 years ago, a friend of mine from Qatar asked me how much he could import a few products including olive oil. Qatar and the surrounding countries can be a good opportunity for you.