Not since the 1958 World Cup, have Wales achieved that, but they are one of the sides hoping to benefit from UEFA's new 24-team format for the European Championship.
If the start to their Euro 2016 Group B programme was tentative, with a late goal by Real Madrid's Gareth Bale required to win 2-1 away to Andorra, victory at home to Bosnia on Friday would establish them as strong contenders.
With Belgium clear favourites to win the group, Wales are expected to contest the second automatic qualifying spot with Friday's opponents, plus Israel and Cyprus.
Coleman was part of the so-called Welsh golden generation that included players like Liverpool's Ian Rush and the Manchester United pair Mark Hughes and Ryan Giggs.
But they failed to qualify for a European Championship or World Cup.
"What a team that was but we did not do it," Coleman told reporters ahead of Friday's game.
"We are good enough to do something we have never done. We can create history.
"If a bit of luck comes our way and we perform and handle the pressure then this can be our golden generation."
The Football Association of Wales is expecting a crowd of more than 30,000, the biggest for three years, to cheer on a team missing a number of players, including Arsenal's Aaron Ramsey and Liverpool's Joe Allen.
Bosnia have already suffered a blow by losing their opening game 2-1 at home to Cyprus and cannot afford defeat in Cardiff even at this early stage.
(Writing by Steve Tongue; editing by Justin Palmer)
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