Despite the Proteas' deep resources of talent, the country has only won one international title -- the Champions Trophy back in 1998.
In World Cup knockout games, they have won just one in 10 and have never made a final, be it in the 50-over or T20 format.
"The near misses in the past, they belong to the people who missed them," insisted Walter.
"This team is a different team. We own whatever is ours to own. And so, our nearest reflection point is this tournament where we've managed to get over the line. So that's what we think about."
South Africa have won all of their seven matches at this World Cup but have consistently struggled to get over the line.
In the first round, they defeated the Netherlands by four wickets only after being 12-4 at one stage and chasing just 104 to win.
A four-run win over Bangladesh followed before they avoided what would have been a seismic shock in a one-run victory over Nepal.
In the Super Eights, they squeezed past defending champions England by just seven runs.
"It's always great to dream and I think everyone in South Africa dreams of the time when a trophy gets lifted," added Walter.
"No doubt that will happen. Whether it's going to be this week, that remains to be seen. We're just going to try and play the best game of cricket that we can. And we still haven't played our best game yet."
South Africa have defeated Afghanistan in their only two other T20 meetings -- by 59 runs at Barbados in the 2010 T20 World Cup and 37 runs in Mumbai six years later.
However, Walter admits that the 2024 Afghanistan team -- who stunned Australia on their way to a maiden semi-final spot -- are a vastly better unit.
"We're seeing Afghanistan in a T20 semi-final. It's awesome for the game of cricket. I love the way they play the game and the way they support it," said Walter.
The coach also dismissed worries over opening batsman Reeza Hendricks who has a top score of 43 at this World Cup.
Hendricks has four scores in single figures including two first-ball ducks against Bangladesh and West Indies.
"Reeza's form doesn't bother me at all. He's a quality cricketer," said the coach.
"It was just three and a half weeks ago that he scored a magnificent 80 against the West Indies (in a pre-World Cup game), a man-alone performance really.
"He's a wonderful cricketer and good batsmen are just one shot away from contributing to the team and that's all we are interested in is giving him the freedom to do that."
