The young Magpies make the long trip to the Robins High Performance Centre (kick-off 1pm GMT) for their first of six consecutive cup matches in a group involving Crystal Palace and Sheffield United's second-string sides, with Newcastle facing their three opponents home and away.
With two teams gaining qualification to the last-16 stage, Brown - who joined Newcastle's academy at the age of 14 - is keen to claim maximum points against their City counterparts, who currently occupy top spot in Group South of the Professional Development League.
The Ponteland-born shot-stopper told nufc.co.uk: "We've been preparing for it all week so we're going to try to make the strongest start possible. We'll go into the game looking to get three points.
"Playing different opposition that we're not used to facing in our league should be good for us and we can compare ourselves to see how we get on against them. It'll be good to see how we perform.
"It is a bit like a tournament as we're playing all the games back-to-back. It's something new for us and will be a good experience.
"Our goal is to qualify for the knockout stages so getting off to a good start will give us confidence going forward into the next group games and, hopefully, progressing further in the competition.
"We've been speaking about this week and we really want to try and push to go as far as we can this year. Any game which you gain experience from is important when you're a young lad coming through.
"To get a trophy at the end would be the cherry on top and would make it a very good season for us."
Newcastle's youngsters were unable to extend their encouraging unbeaten run in the Premier League 2 run to seven matches following a 4-2 defeat away at Division Two leaders Leeds United.
Brown, who signed his first professional contract with his boyhood club in the summer of 2020, admitted the squad were frustrated not to end their Premier League 2 campaign for 2022 on a high but remained confident of recovering from their slight setback earlier this week.
The 20-year-old goalkeeper added: "It was disappointing to see our six-game unbeaten streak come to an end. We've reviewed the game as a team and seen what we can do better going into the next game on Monday. We'll just have to keep our heads down and keep working.
"We wanted to go and take three points, making a statement on the league as Leeds are unbeaten this season and top of the table. That didn't happen but that's football, sometimes, and we just need to focus on the next match.
"We had our fair chances in the game. I thought it was pretty even during the match but it was down to Leeds taking their chances when we didn't."
