German coach Bernd Storck has got rank outsiders Hungary finally looking to the future not the past and even as they face a huge task against Belgium in the last 16 of Euro 2016 on Sunday, he says it has been "a dream come true".

Before the tournament, the 53-year-old told AFP that third place in the group behind heavyweights Portugal and Austria was the height of Hungary's ambition.

But a shock 2-0 win over the Austrians in the opener and then a draw against Iceland booked a place in the next round even before the Hungarians were involved in the most thrilling match of the tournament, the 3-3 draw with Cristiano Ronaldo's Portugal.

Against all the odds, Hungary finished top of Group F in their first European Championship finals since 1972 and, indeed, their first major tournament since the 1986 World Cup.

"Hungarian coaches tend to opt for safety, but I am a different character," Storck said before the tournament.

"He has made the team believe in themselves, it is a new thing," Gyorgy Szollosi, editor of the Hungarian edition of the FourFourTwo magazine, told AFP.

Since the journeyman coach was appointed in 2015, Storck has tried to change the mentality of Hungarian players, telling them to stop looking backwards to the glory days. "The shadow of the past on Hungarian football is enormous," he said last week.

But in France, his team has looked very much to the future and records have been tumbling.

The win against Austria was Hungary's first over a European team at a major tournament since 1966 and their first victory at a European Championships since 1964.

Not since 1966 had they qualified from a group stage.

The displays have led to jubilation from success-starved fans in Budapest.

Some have even resurrected the nickname "Magical Magyars", a nod to the legendary 1950s team led by Ferenc Puskas.

Storck's boldness was already evident in the qualifying playoff against Norway last year when he gambled by handing an international debut to 22-year-old Laszlo Kleinheisler, who had hardly played a game all season at his Hungarian club.

The fearless redhead though scored a crucial goal, and was soon snapped up by Bundesliga side Werder Bremen.

Storck also gave a key role to 21-year-old Ferencvaros midfielder Adam Nagy, now sought after by clubs like Benfica and Marseille due to his impressive performances at Euro 2016.

The veteran players too have handsomely repaid Storck's faith.

A long-range strike by 37-year-old former West Brom midfielder Zoltan Gera in the thriller with Portugal was voted goal of the group stages by UEFA.

Balazs Dzsudzsak, 29, who kept the captain's armband despite scoring just three goals all season with his Turkish club Bursaspor, scored two goals in the same game.

The 40-year-old goalkeeper Gabor Kiraly, the oldest player ever to play at a European Championships, has meanwhile delighted fans well beyond Hungary with his clowning about and grey tracksuit trousers as well as his saves.

Storck had been advised to use Kiraly as a goalkeeping coach, but the German insisted that his experience was invaluable on the pitch.

And true to Storck's pledge to encourage a more attacking mentality, no team scored more than Hungary's six goals in the group stages.

According to Szollosi, a key element of the team's run has been its preparation which began a month before the tournament and helped to build team spirit.

Unlike most of their Euro 2016 rivals, none of the Hungary squad play for top European teams involved in the later stages of the Champions League or Europa League.

"They are strong not just mentally, but physically as well, scoring crucial goals late in games, as against Austria and Iceland," said Szollosi.

"It's all been a fantastic surprise."