In Round One, goals from midfielders Kallum Fuller-Thompson and Jubilee Ntege completed a 3-0 victory over Berkshire neighbours Bracknell Town on October 27.
The Robins are the next to face up against Harrison Gilkes’ side on Wednesday evening, with Premier League and Championship sides entering at Round Three.
Speaking ahead of the cup tie, academy manager Michael Gilkes told RoyalsTV: “It was a local derby, and they made it very difficult for us, posing a few problems at times.
“We are really pleased just to get through; it was really competitive.
“Unfortunately, we lost a couple of players through injuries, so they will be out for two or three months, but that is part of football so no excuses. It gives an opportunity for others to make a claim for themselves.
“There was fantastic support in Round One against Bracknell, they brought a few down being local. Cheltenham is only an hour or so, so if anyone can come out and support the younger players next week, it would be very much appreciated.”
The most prestigious youth cup competition in world football since its beginning in 1952, the Royals reached the semi-final in 2014. Falling at Round One last season, Mikele Leigertwood’s side reached Round Five two years ago, narrowly losing to Manchester City.
Gilkes and his team are hoping to put together another strong run this time out.
He added: “At youth level, if you’re Under-18 and take Andre Garcia out of the equation, getting the opportunity to play in the stadium is a big deal.
“The FA Youth Cup is the biggest competition you can have at that age, so it’s a big game for those players and you try to make positive memories from it.”