The English mentor says they will draw inspiration from their win and a draw against Nigeria during their road to the biennial showpiece.
"I don't want to say this and bring pressure onto the players, but I don't think this squad of players that we have at the moment should fear anybody," Baxter said.
"I will be saying to them that no matter who is on the other side of the field, we can beat them,” he added just after their arrival at OR Tambo International Airport on Tuesday.
With the South African football fraternity expecting a lot from the national side, Baxter says his team must accept that responsibility and go to do well in Egypt in June.
The 1996 African champions opened their Group E qualifying campaign with a 2-0 win over the Super Eagles before playing to a draw at home.
"I don't think Nigeria will be scared of anybody and we just beat them and drew with them, and I think that my players can go there without any fear,” continued the coach.
Meanwhile, all eyes are now focusing on the draw for the tournament that is set to be conducted on April 12 and the coach is confident his charges will be able to handle pressure and expectations.
"There will always be expectations but we've got to make a friend of that," he concluded.
Although the Southern Africans finished as runners-up behind the Super Eagles, they amassed 12 points from six games, they won and drew three times and finished their group stage assignments without a defeat.
Bafana received a heroes’ welcome during their arrival from Tunisia where they beat Libya 2-1 on Sunday and the tournament will be played between June 21 and July 19 2019.