The young Magpies booked their place in the last-eight after finishing in top spot of Group C, picking up a total of eight points after victories against FC Halifax Town, Tamworth and Gateshead.
Thompson, who signed his first professional contract with his boyhood club in the summer of 2023, is hoping United's second-string can take inspiration from their positive group campaign ahead of facing the Robins, who currently occupy the play-off spots in the English fifth tier.
The 19-year-old defender, who joined United's youth set-up as a 13-year-old, told newcastleunited.com: "These games are really important for us as an under-21s side because you're in for a real game, playing against senior opposition which is good experience for the lads.
"It's a big test as we have quite a young squad and we're coming up against players who have most likely dropped down into the National League but it'll be a great experience to play against that kind of team, who will mix it up compared to possession-based teams in the Premier League 2.
"We can take confidence from the group games and we've shown we can do it after topping our group with a few wins against the senior sides. Hopefully, we can take those experiences into the next game and progress into the semi-finals."
Newcastle's youngsters will be key to record their first win of the calendar year and face an Altrincham side who, last weekend, suffered their first defeat on home soil since August following a 2-1 loss against AFC Fylde.
Thompson, who featured for Eddie Howe's first-team side last term during the club's post-season matches in Australia, is relishing the challenge against the highest-ranked National League outfit remaining in this season's competition (sixth).
"We've seen some clips of them and they look like a good side," he added. "They're challenging for the National League play-offs but I don't think we'd have it any other way. To be the best, you've got to beat the best so we're really looking forward to it.
"At the start of the season, we set out to go far in the cup competitions as well as getting into the top 16 of the Premier League 2 to get into the play-offs and we're on track with all of them at the minute."
Tickets for Newcastle United Under-21s' National League Cup quarter-final tie against Altrincham can be purchased here and the cup game will also be streamed live on National League TV.
