The Croatians face tough Euro 2012 group stage opposition in holders and world champions Spain, Italy and a newly resolute Ireland.
Their path to the quarter-finals in 2008 was considerably easier.
Having beaten co-hosts Austria, Poland and eventual runners-up Germany four years ago, the Croatians took the lead against Turkey in the final minute of extra time of a pulsating last-eight clash in Vienna.
As thousands of Croatians celebrated, they conceded an equaliser with the last kick of the game and then lost the penalty shootout.
Their confidence dented, Croatia failed to reach the 2010 World Cup and endured a patchy Euro 2012 qualifying campaign before gaining revenge against the Turks in a play-off.
They finished second behind Greece in their group before producing their best performance of the campaign in a 3-0 win in Turkey in the play-off first leg and confirmed their passage with a goalless draw in Zagreb.
Many of the Euro 2008 squad remain and form the backbone of the current team in which goalkeeper Stipe Pletikosa, defenders Josip Simunic and Darijo Srna, midfielders Niko Kranjcar and Luka Modric and striker Ivica Olic are regulars in Bilic's preferred 4-4-2 formation.
Especially influential are 30-year old captain Srna and playmaker Modric, who has flourished at Tottenham Hotspur for most of this season until he and his team faltered in the closing stages of the campaign.
Like most Balkan teams, Croatia have plenty of natural talent. What separates them from their regional rivals, however, is the ability to play well under pressure.
Since gaining independence from the former communist Yugoslavia in 1992, the Croatians have qualified for seven of nine major tournaments and stunned the world when they reached the semi-finals of the 1998 World Cup in France.
Coach Bilic was one of that team, which included Zvonimir Boban, Robert Prosinecki and Davor Suker, all of whom enjoyed impressive careers and won the Champions League.
The present generation is led by Srna, Modric and Brazilian-born striker Eduardo da Silva, who has made a successful return to international football after an horrific career-threatening injury while playing for Arsenal.
They possess some of that 1998 talent and guile, but may lack adequate replacements for ageing key players. This could be a weakness for the squad.
Bilic's team may struggle to match the Spaniards and Italy for pace and crisp one-touch passing. So, should they fail to beat Ireland in their opener in Poznan on June 10, hopes of a last eight place may be wrecked.
Weaknesses exposed in the qualifier were made more obvious in February's 3-1 home defeat by Sweden in a friendly, when AC Milan striker Zlatan Ibrahimovic exploited a flat defence with deadly ease.
Croatia's build-up play is usually crafty, but against top-level opposition it can be slow and predictable, another weakness they must overcome if they are to progress by harnessing their spirit and determination in the tournament.