Not since Euro 2000 - where they went out in the group stage without a single victory to their name - have Slovenia competed at the continent's top competition, but their performance in qualifying offers hope of Kek's men springing a surprise in Group C.
Indeed, Slovenia won seven of their 10 preliminary fixtures en route to a second-placed finish behind Denmark, who will be one of their three group foes in Germany alongside Serbia and England, one of the favourites to go all the way.
Before attempting to pick up their first-ever Euros win as an independent nation, though, Slovenia will meet Armenia and Bulgaria in a pair of warm-up matches, taking on the former on June 4, four days before a meeting with the latter.
From a modest selection of 30 players - at least four of whom will be culled - a few names still stand out, and here, Sports Mole picks out some of the Slovenian players to watch at this year's European Championships.
Benjamin Sesko
One man who has already put himself in the shop window ahead of Euro 2024 is RB Leipzig's embryonic attacker Benjamin Sesko, who will add a few more pounds to his value should he shine in Germany next month.
A product of the famed Red Bull Salzburg academy, Sesko initially struggled to adapt to life in the Bundesliga but hit an extremely rich vein of form in the closing stages of the season, scoring in each of Leipzig's last seven top-flight matches of the campaign to end with a respectable 18 goals.
Standing at 6ft 4in tall, the 20-year-old - who celebrates his 21st birthday on May 31 - also shone for Slovenia in Euro 2024 qualifying with five goals in the section, second only to Rasmus Hojlund's seven, and he boasts a total of 17 direct contributions in 28 appearances for his nation.
Both Arsenal and Manchester United are said to view Sesko as a prime attacking target for the summer transfer window, but Leipzig are fighting tooth and nail to keep hold of the aerially dominant striker, who is sure to give Harry Maguire a proper run for his money from set-pieces.
Jan Oblak
Long heralded as one of the finest glove-wearers in the men's game, Atletico Madrid stalwart Jan Oblak will sport the captain's armband for Slovenia at this year's European Championships, and it is easy to forget that he is still only 31 years of age.
Oblak could therefore have another decade of football left in his legs and is poised to win his 65th cap for the national team during their opening contest with Denmark; from his opening 64 matches in a Slovenia jersey, the goalkeeper has kept a respectable 30 clean sheets.
Due to Slovenia's recent failures on the international stage, Euro 2024 will represent Oblak's first major tournament for his country - whom he has skippered since 2020 - and the former Benfica man already has four Slovenian Player of the Year honours next to his name.
Soon to celebrate his 10th anniversary as an Atletico Madrid player, the 6ft 2in shot-stopper has not been one of the best goalkeepers on the planet in a statistical sense this term - now being overshadowed by the likes of Alisson Becker and Emiliano Martinez - but his presence in between the sticks remains as intimidating as ever.
Josip Ilicic
Remember him?
A cult hero of Serie A, experienced striker Josip Ilicic was formerly the heartbeat of the free-scoring Atalanta BC side before and during the behind-closed-doors era, forming that fearsome attacking trident with Luis Muriel and Duvan Zapata and excelling in both a scoring and playmaking sense.
The 36-year-old reached double figures in three straight Serie A campaigns - few can forget his four-goal haul against Valencia in the 2019-20 Champions League either - and also laid on 10 assists in the 2020-21 season, but he called time on his Atalanta career in 2022 after struggling with mental health problems.
Ilicic has since rediscovered his golden touch in his homeland with Maribor - laying on eight goals and 11 assists in 31 Slovenian PrvaLiga matches in the 2023-24 season - and he is the second-highest capped player in the Slovenia squad with 79 appearances to his name.
In that time, the wily attacker has chipped in with 16 goals and 17 assists, and his preliminary call-up ended his two-year absence from the national team since his last appearance in November 2021; a welcome sight for fans of Slovenia and fans of football.
Slovenia Euro 2024 preliminary squad in full:
Goalkeepers: Jan Oblak (Atletico Madrid), Vid Belec (APOEL), Igor Vekic (Vejle), Matevz Vidovsek (Olimpija Ljubljana)
Defenders: Jure Balkovec (Alanyaspor), Jaka Bijol (Udinese), Miha Blazic (Lech Poznan), David Brekalo (Orlando City), Vanja Drkusic (Sochi), Erik Janza (Gornik Zabrze), Zan Karnicnik (Celje), Petar Stojanovic (Sampdoria), Zan Zaletel (Viborg)
Midfielders: Timi Maks Elsnik (Olimpija Ljubljana), Adam Gnezda-Cerin (Panathinaikos), Jon Gorenc Stankovic (Sturm Graz), Tomi Horvat (Sturm Graz), Jasmin Kurtic (Sudtirol), Sandi Lovric (Udinese), Benjamin Verbic (Panathinaikos), Miha Zajc (Fenerbahce), Adrian Zeljkovic (Spartak Trnava), Nino Zugelj (Bodo/Glimt)
Forwards: Zan Celar (Lugano), Josip Ilicic (Maribor), Jan Mlakar (Pisa), Benjamin Sesko (RB Leipzig), Andraz Sporar (Panathinaikos), Zan Vipotnik (Bordeaux), Luka Zahovic (Pogon Szczecin)