The Central Americans were given no chance when they were drawn with Italy and England eight years ago in Brazil but ended up topping the group as the two heavyweights went home.
Costa Rica reached the quarter-finals that year, losing to the Netherlands on penalties, but their hopes of similar heroics this time seemed remote after a 7-0 thrashing by Spain.
They bounced back to beat Japan and a win over Germany on Thursday would send them through to the last 16.
Costa Rica could even go through with a draw, if Spain beat Japan, while four-time world champions Germany simply have to win.
"Eight years have gone by and players have changed but you have good memories," Colombian Suarez, who took charge last year, told reporters on Wednesday.
"Maybe it's down to the genes of the Costa Ricans. When they reach a World Cup they do things differently and they play well. I'm not just talking about 2014 in Brazil, I think also in Italy 1990 they reached the last 16 when no one believed in them.
"They are never the favourites, which is good."
Suarez said his team were fully aware that a Germany side fighting for World Cup survival will be dangerous but said his side were "excited and eager" with a clear objective.
"We need to be emotionally strong and break our backs in this match. Of course, if Germany is knocked out it would be a major thing and we would be proud to be responsible for that."
Midfielder Celso Borges (34) is one of the survivors from the side that reached the 2014 quarters, along with keeper Keylor Navas, striker Joel Campbell and midfielder Yeltsin Tejeda.
He said recovering from a "crushing" defeat by Spain had not been easy but believes the squad could make history again.
"We have the utmost respect for Germany," Borges, who has a record 157 caps for his country, told reporters.
"But it's all down to us and if we learn from our mistakes in the last two games we have good vibes and good energy.
"I think it's a huge motivation for us. I think this could be a historical moment for us."
First female referee is 'positive step' says Suarez
Stephanie Frappart's (38) appointment as match referee for Thursday's crunch clash between Germany and Costa Rica is a step forward for women in a "sexist sport", according to Costa Rica manager Suarez.
Frenchwoman Frappart will make history as she leads the first all-female refereeing team at a men's World Cup in the Group E match which Germany must win to keep alive their hopes of progressing to the last 16.
Suarez said it "spoke volumes" for Frappart's commitment to reach the top level in a profession dominated by men.
"I am a great admirer of everything women have conquered and I like the fact they want to keep on conquering things," Suarez told reporters.
"This is another step forward. This speaks volumes for this woman, of her commitment, especially in this sport which is a very sexist one. It's very difficult to reach the point that she has reached, I think it's good for football and a positive step for football, to show that it's opening up for everyone."
Frappart will be joined by Brazil's Neuza Back and Mexico's Karen Diaz as she puts down another marker for female officials having also been the first woman to referee a men's World Cup qualifier in March.
Last week, she became the first female official at a men's World Cup when she was the fourth official for the Poland v Mexico Group C tie, but on Thursday she will be more in the spotlight.
Borges also welcomed her appointment for such a high-profile game.
"I think it's great and it's a huge achievement for women globally," Borges, who is playing in his third World Cup for the Costa Ricans, told reporters.
"If she is there it's because she has all the capabilities to perform on this stage. She has done it before in big matches so I don't see why tomorrow should be an exception.
"I just hope she has a good match and that we can help her make it an easy match."
Her appointment was also backed by Germany manager Hansi Flick who said he had "100% confidence" in Frappart.
"She deserves to be here based on her performance. I hope she is equally looking forward to the game just like we are, and I hope she can deliver a good performance," he said.
Germany defender Lukas Klostermann (26) also welcomed the move, which he described as "the most normal thing in the game."
"I have never looked prior to the game if it is a man or a woman that will be with the whistle, and I hope it will remain a normality," he said.
