The Hammers are just one point from ending a remarkable season in sixth place with the club's all-time record for Premier League points.
Their form this season has forged a team spirit unlike anything players have seen at the club before. Without the usual ability for trips abroad or team nights out, Moyes and his staff have taken a more old school route - with coach Stuart Pearce becoming the club quizmaster.
"On the journey we've had some incredible quiz nights, set up by Pearcey," said Moyes. "We have been fighting each other on the tables.
"Small things, we've not been doing anything special, but it’s helped the group. We had to build towers with marshmallows and uncooked spaghetti. It’s just a marshmallow fight.
"We have had good times amongst us. The boys have got a few songs after wins they are putting on in the dressing room and it’s real fun. We’ve had some great moments."
Those great moments have driven West Ham to the brink of Europe. They are all but secured a place in the Europa Conference League - the new third-tier Uefa tournament - but are aiming higher. Avoid defeat against Southampton on Sunday and the club will be in the Europa League next season.
Years after the owners spoke of taking the club to the next level at the London Stadium, Moyes looks to be getting there. Now he wants the board to give him the trust to take them even further.
"I think this is the new level for West Ham," said Moyes. "The new level for West Ham has to be being competitive in the league, it needs to be. And that doesn't mean that we are guaranteed that we are going to be competing at the top every year, it doesn't mean that but I think competitive means being the new West Ham which is going to try to be competitive and we're gonna try and look at ourselves as a club at the top end of the league. That's what I want to do.
"I think that's what I see, the growth and the opportunity. I think this club can do that. The reason why I think they can do it is because of the fan base, because of the location, because of the history. But I think we also now need to say we have to find our way of doing it here.
"I'm not asking for time, I don't think any manager can ever ask for time. But I think if you're ever going to give a manager time it would be now, where somebody has come in and saved the club twice, had one year and got ourselves in a position where we're gonna challenge for Europe
"Now, if you are ever gonna trust and say let's go to the next level, now you've got to give that trust over, you've got to give that to the manager, the ability to try to push the club on to reach what you see as the next level.
"I think we're at the new level now and I think we've got to make sure that we stay there."
The 10,000 fans returning to the London Stadium on Sunday will see a very different West Ham side to the one that last played in front of such numbers.
The Stratford stadium has long been a place which can turn toxic quickly if things aren't going well - and having forged a strong spirit within the playing group, Moyes now wants to see that reflected in the stands.
“We have tried to work in this pandemic to get a good team spirit,” said Moyes. “Anyone who knows us will see there is a fantastic spirit. What we need is that fantastic spirit from the terraces now as well, from the supporters. We need to build on it.
“We need positive around the club. I’m going to try and do that I’m going to try and keep building it, I’m going to be positive, I want the supports to be positive.
“I want all the new young supporters who are going to come in for West Ham in the future to see a good team. I want them to come to an environment which is positive, and they can enjoy coming to.”