With Italy and Ireland also in Group C, Croatia face a daunting challenge if they are to match their achievement of four years ago when they topped their qualifying group with three wins including one over eventual runners-up Germany.
It is a challenge Bilic is relishing, however, as one of the brightest young managers on the international scene pits his wits against the tournament favourites.
"It's a tough group of course but that doesn't mean we don't have a chance," Bilic told Reuters in an interview at a Euro 2012 workshop in Warsaw.
"In football you see surprises week in, week out. Spain are the best side and they were in the last World Cup but Switzerland beat them and they had some troubles with Chile, Paraguay and Holland - they weren't cruising.
"They didn't have it easy in 2008 either, especially against Italy [whom they beat on penalties in the quarter-finals after a goalless draw].
"They are a great team, great champions and worthy favourites but they are not going to walk through the championship with a cigar."
Bilic, who still plays guitar in a rock band, generally has the look of a man who has spent the night partying hard on the tour bus, but behind the unkempt demeanour he is one of the most charming men in the game.
A law graduate and fluent in four languages, he is also one of the most intelligent and thoughtful.
Understandably, he declined to discuss his preferred tactics against Spain but said they were the one team against whom your own preparations counted for little.
"When you play against Spain it's more up to them than up to you," he said. "It's like Barcelona - we've all seen how in the last four years teams have tried everything. Some have tried to attack them and they lose, some have played a normal game and they lose. Most teams try to defend against them but they find a way through.
TOUGHEST GAME
"It may sound like a contradiction but though Spain is the toughest game it is the easiest to prepare for. You are almost reduced to one way of playing - trying to break them up without committing too many players.
"We all have different ideas on how to counter them but really it's up to them. You won't have more possession than them so your options are reduced but you can harm them.
"They are playing the best football and it's nice to watch but they have had games where they have struggled so you can get at them."
Croatia's three opponents will certainly be expecting a stiff examination from a team who, in their short existence, have become a consistent tournament presence with enough technical ability and mental resilience to beat the best.
Bilic was a member of the team that finished third in the 1998 World Cup six years after joining FIFA as an independent nation and took over as coach in 2006 when he was still only 37.
He began well by topping a tough Euro 2008 qualifying group ahead of Russia and England and continued the good work once the tournament began.
