The 2004 European champions have now gone three games with a goal, so will therefore be intent on picking up a morale-boosting win in their final fixture before flying to Brazil
Greece will aim to end their lacklustre World Cup build-up with a positive result against Bolivia in New Jersey on Friday.
After qualifying for their third World Cup with victory over Romania in the European play-offs, Fernando Santos' men have failed to score a single goal in their following three outings, with the last two ending as goalless draws against Portugal and Nigeria.
Santos, though, is remaining positive about their chances of springing a surprise or two
Greece, like many nations gearing up for World Cup, are in the United States to acclimatise themselves to conditions similar to the ones that await them in Brazil.
New York Red Bulls' Red Bull Arena will provide the backdrop for Greece's final game before heading to South America.
And the signs look promising that Santos' side can boost their confidence with a much-needed victory, despite their goal draught, as Bolivia are winless since the start of February, a barren spell that has stretched 10 games.
"We have accumulated a little bit of fatigue, but generally we are adapting well to the climate," said Santos after Tuesday's clash with Nigeria.
"These tests are important to ensure we are prepared for the first match with Colombia.
"We cannot play in Brazil so the best alternative is to adapt ourselves in another way, the United States have similar conditions to the ones we will confront in Brazil so it is normal for teams to adapt in time difference and weather conditions.
"I believe the two 0-0 draws have had different meanings, we are playing better, it is part of the progression we want to see.
"I am satisfied by the effort from the players."
The two nations have never met before, but, with Colombia being Greece's first opponents at the World Cup, Santos will hope that Bolivia can give him an insight into the South American way of playing.
After Colombia, Greece face Japan and Ivory Coast as they look to escape from the group stages for the first time.