"I hope we will be very competitive with Nigeria. We will give them a game," Baxter told a press conference after his unveiling in Johannesburg on Monday.
The Englishman was appointed earlier this month as a replacement for Ephraim 'Shakes' Mashaba who was given the boot in December last year.
He will start his second spell as Bafana Bafana head coach with a 2019 Africa Cup of Nations qualifier against the Super Eagles in Uyo on 10 June.
Baxter, who signed a five-year contract, said he will name his technical team and squad for the Nigeria game on 25 May.
"We need to be competitive and players will do it the South African way; that should reflect the play in the country," said Baxter, who previously coached the 1996 African champions from May 2004 to November 2005.
The 63-year-old, who will continue to coach Premier Soccer League side SuperSport United until the end of the season, said there was no shortage of talent in South Africa.
"I believe the nation has enough players to succeed and I also believe in my abilities; I'm very optimistic," said the former Kaizer Chiefs boss.
He added: "I'm really looking forward to this latest challenge. If I wasn't ready, I would not have accepted the challenge.
"I'm very optimistic if we can pull together, but don't be too negative because it will affect everyone. I'm asking for buy-in from every South African.
"I will be going abroad to watch players who ply their trade there. I will watch every South African. They will get a fair chance.
"I want Bafana Bafana to unite South Africa in the long term. If we do that we will become a powerhouse of football," said Baxter.