The Magpies' second string defeated Doncaster Rovers, Notts County and Grimsby Town in the group stage before overcoming Macclesfield Town on penalties to book a last-16 meeting with the Black Cats.
And Gibson, part of Newcastle's academy since the age of 11, is optimistic that United can continue their road to Wembley with a positive result at the Stadium of Light, with a place in the quarter-finals at stake.
The Stanley-born defender is now keen for the youngsters to claim a derby win over Sunderland's senior side and feels United have proved a point during their run in the competition.
"The mood is very positive," Gibson told nufc.co.uk. "Obviously, there are a few nerves as we know there is going to be a big attendance and we haven't played in front of a crowd as big as that before, but it can also be a good thing which can work in our favour.
"We aren't used to having a huge away following with the under-23s so everyone in the team has been talking about it and are really looking forward to having such a strong support behind us.
"We just need to look at the match as another game. They are performing well in the league but I think we can get a strong result as we are a very good side and we'll be ready to give our all on the night.
"My first memory of a Tyne-Wear derby has to be when Newcastle beat Sunderland 5-1. I had a season ticket for eight years so that was one of the best games I've witnessed.
"I remember the atmosphere (at St. James' Park) was incredible and it's always nice getting one over on your rivals. It would be unbelievable to create similar memories of our own for the fans.
"It's also a chance to get into a quarter-final and potentially play at Wembley. At the start of the season, if you said we'd reach the last 16 of the Checkatrade Trophy, I think many people would have laughed but I think we have proved them wrong."
Gibson's footballing career was cast into doubt in 2015 after being diagnosed with ulcerative colitis, a condition which causes inflammation in the bowel. However, after 425 days after his previous appearance in a Newcastle shirt, Gibson featured in the under-23's pre-season victory at Barrow in July.
"At one point during my illness, I thought about packing in with playing football completely. I'm now back and have played nearly half a season so I'm very glad that I continued to stick at it," he admitted.
"Being back in the team is unbelievable and if I'd missed an opportunity to be a part of the game against Sunderland, I could never forgive myself for it.
"I would be coming into training feeling lethargic and tired. I never felt like I had the energy to get through a training session. I would still carry them out but I knew in my head that I was nowhere near 100 per cent.
"Towards the end of the 2016/17 season, I would be playing matches but suffering cramp before half-time due to losing so much fluids during the day and when it got to the evening, I had nothing left to give.
"Fast forward and I have been playing two to three games a week in a full month. We've had a break for Christmas and I'm now feeling very good and looking forward to the second half of the season.
"When I was ill, I didn't feel part of the group in a footballing way even though I was with the players during training. The lads were normal with me but it was just from my own perspective.
"Even being involved in the changing rooms amongst the lads again is excellent and I'm really enjoying it. I now take a completely different approach to playing football then what I did in the past.
"Before my illness, sometimes I would come into training and I may have taken it for granted at times, coming into work and not feeling very motivated. Now, I feel like I'm coming into work everyday with a positive attitude for training."
Tuesday night's game will be shown live on NUFC TV. Read more here.
