The Crusaders are preparing to play in the finals of a European Championship for the first time, with their tournament opener coming against Turkey on June 18.
Willy Sagnol's side will also tackle Czech Republic and Portugal in Group F this summer, and Kvaratskhelia has opened up on Georgia's achievement ahead of Euro 2024.
"It was the greatest dream of every Georgian to become a part of such an important tournament, and it was the happiest day for all of us when we achieved it," he told UEFA's official website.
"But we didn't come here just to attend; we wish to leave our mark on EURO 2024, to write a new page of history. We will do our utmost for this. Our team is very focused and ready for this tournament. In Georgia, everyone is waiting for our debut. I think on 18 June, we will see Georgia united as one and we will try to win."
Georgia will create history at Euro 2024
Kvaratskhelia, who plays his club football for Italian giants Napoli, also spoke about the pressure that comes with being considered as the team's star player.
"This is a very big responsibility, and I am grateful when my work is appreciated. There are a lot of Georgian footballers who could become the best player of the country; every one of us tries to be a team, and individual success is less important to us at the moment," he added.
"We are very focused and will do our best to succeed. It's a pleasure for me to play at EURO 2024. These are unforgettable moments and emotions which we will remember for the rest of our lives.
"We have a mix of experienced and young players, and we have gelled very well. We have become one big team that is able to fight anyone. [Centre-back and captain] Guram Kashia is a good example for all of us. He is experienced and older than us and exercises every day.
"He provides an example to younger players to work hard every day. He is a real captain and all we can say to him is: thank you. He is leading us and does everything a real captain should on and off the pitch."
Kvaratskhelia sets out Georgia's aims for Euro 2024
The 23-year-old said that Georgia's aim this summer is to progress through the group stage, with a strong third-placed finish also capable of seeing them advance to the knockout round.
"Preparations are at maximum intensity because there is not long to go before our dream - the first match in the EURO for Georgia's national team, and we are loaded with emotions," he said.
"But we are trying to control these emotions. We are preparing as best as we can for the first game, which is the most important because we will keep on going with the same mood as we begin.
"Our first goal, just like every other team probably, is to go past the group stage and we will do everything to achieve this. I hope the game ends in our favour and our goal will be achieved."
Georgia will enter the tournament off the back of three straight wins, including a 3-1 success in their only warm-up friendly against Montenegro on June 9.