Away wins at Arsenal, Liverpool and Manchester City have grabbed the headlines while the club's new additions, like Dimitri Payet, Manuel Lanzini and Moses, have Hammers fans excited about the future.
But the fans aren't the only ones expecting big things.
Moses was loaned out by Chelsea boss Jose Mourinho once again this season, but not before signing a new long-term deal with the Blues.
Exciting atmosphere the key
But he is fully focused on the Hammers and has told the club's official website the key to the side's early success has been the atmosphere created by Bilic.
"I have been very impressed by the start we have made and very excited as well," he told whufc.com.
"We have got a good manager here and everyone wants to play for him. We are looking forward to every game.
“We know where the club finished last year and if we can do even better this year it will be a massive bonus for everyone.
“But we believe in the quality of players that we have both collectively and individually and we just need to keep working hard in every game.”
Moses makes West Ham dangerous
Moses has already proved a welcome addition to the West Ham team.
Last season, the likes of Alex Song were often ready to play a killer pass but did not have team-mates of sufficient quality to read what he was trying to do.
And for Slaven Bilic's strikers, like Diafra Sakho, Andy Carroll and Nikica Jelavic, Moses should quite literally mean goals.
The wing man is very unselfish and, when he's not tracking back to help out his team-mates, he will be terrorising his opposing full-back with a view to supplying the strikers with ammunition to get their goals.
The new West Ham forward is also not afraid to have a go himself, often coming up with the odd cracker, like in the Hammers' 2-1 win up at Manchester City, when he cuts inside off the wing.