West Ham are into the fifth round of the competition for the first time since they made the move from Upton Park to the London Stadium, and face a big hurdle in the last-16 with either Manchester United and Liverpool awaiting them. But few will want to face Moyes' side in this shape.
The Hammers are playing with confidence and without fear, brushing aside League One Doncaster Rovers 4-0 with a professionalism not seen at West Ham until Moyes got to grips with the club. The 4-2 FA Cup defeat at AFC Wimbledon under Manuel Pellegrini feels a long way back now.
Saturday's victory made it five wins on the trot, and seven without loss in all competitions. It may not be the most impressive list of sides defeated since the turn of the year - Everton, Stockport, Burnley, West Brom and Doncaster - but the Hammers have rarely looked in trouble, and Moyes knows they have another level to hit.
A sixth win in a row at Crystal Palace on Tuesday could lift West Ham into the Premier League top four. The visit of champions of Liverpool will then provide a chance to show just how far this side have come under Moyes, while offering a test run of a potential fifth-round tie.
Winning the Cup would be some feat - even reaching the latter stages given the next tie - and there is some way to go yet. But in a season like no other, the chance is there - and it is tantalising.
West Ham have no relegation battle to distract them this time around and, striking department aside, have the depth to go the distance with some luck. The foundations are there, and the whole squad is stepping up.
Moyes made changes but still put out a strong side on Saturday, with the performance allowing the Hammers boss to hand out a trio of debuts: goalkeeper Nathan Trott, midfielder Jamal Baptiste and forward Oladapo Afolayan, with the latter scoring the Hammers’ fourth to cap a “dream” day for the 23-year-old.
"I know my family would have been at home watching... When I left this morning my dad was just sat in the front room with nothing on the TV – I think he was more nervous than me!"
This interview from @dapo_afolayan ❤️ pic.twitter.com/R7ikYojVNT
— West Ham United (@WestHam) January 23, 2021
"We have used the squad today but we haven't used a whole load of kids from the start of the game," said Alan Irvine, Moyes's assistant. "We have used a squad of Premier League players who have a lot of experience, so we certainly weren't looking at this as the sort of game where we could put out a weakened team.
"We know what is coming over the next few weeks and we know the importance of being able to spread the demands amongst the whole squad, and fortunately, the players who came in today did extremely well."
The performances of Andriy Yarmolenko - leading the line in place of the rested Michail Antonio - and Said Benrahma will have been encouraging.
Moyes has called on the latter to step up in recent weeks and while the search for a first goal since his move continues, the Algerian impressed and claimed an assist. One goal could spark him into fine fettle.
"It would certainly help," Irvine added. "People know that we brought Said here to create goals and to score goals; that is the type of player he is, so we are obviously hoping for him to do that.
"He has created some goals during the time that he has been here, but he like everybody else is desperate for him to get that first goal and of course that would settle a lot of things down."