ADDIS ABABA, Ethiopia — Less than a week before the most important match in its history, Ethiopia’s national soccer team trained on a wet, uneven field on the outskirts of the capital. Nearby, a woman hung her wash on a clothesline. Birds of prey circled overhead, and sometimes a plane flew past at low altitude, coming from the capital’s busy airport, which a few months ago added a connection to Rio de Janeiro.

The timing could not have been better. Ethiopia will face Nigeria on Sunday in the first leg of one of five home-and-home playoffs that will determine the five African teams in next summer’s World Cup in Brazil. A few years after it was barred from even attempting to qualify for the 2010 World Cup, Ethiopia is two games from reaching the tournament for the first time.

“We have played against Nigeria many times,” Ethiopia’s coach, Sewnet Bishaw, said at a luxury hotel in the city center, where the team has been living as it prepares for the match. “Even though Nigeria is a big nation, a big country with huge, skillful and professional players, we’ve become very strong in the past few years.”

The African playoffs include many of the World Cup regulars — Ghana, Ivory Coast, Cameroon — that have for years fed talent to Europe’s top clubs and leagues. The presence among them of Ethiopia, a persistent underdog that won its only African championship a half-century ago, is among the biggest surprises of the current qualifying cycle. But a string of good results, a rare bit of stability in its national federation and a focus on youth development have many in Ethiopia, Africa’s second-most populous country, feeling as if a sleeping giant has been awakened.