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Manager Sam Allardyce maintains West Ham must use the next couple of weeks to show they are not just "all about Andy Carroll".
Carroll impressed during his debut against Fulham on September 1 following a loan switch from Liverpool, only to limp off in the second half with a hamstring problem which ruled him out of England's World Cup qualifiers with Moldova and Ukraine.
The 23-year-old striker has now resumed light training and could be back in contention for the visit of Arsenal on October 6.
Before then, however, the Irons have some testing fixtures, including a home tie with Sunderland this weekend as well as a Capital One Cup clash against Wigan ahead of a trip to QPR.
Allardyce expects the rest of the squad to step up to the challenges ahead.
He said: "It depends on the likes of Carlton Cole and Modibo Maiga stepping in and doing the business, making sure we use the strength of the squad when we need to.
"We have only got two players injured at the moment, a lot of other teams in the Premier League have more. If that continues it will help for us to be more and more consistent.
"Andy Carroll has only played 68 minutes for us. We have conceded just three goals, all at Swansea, and kept clean sheets in the other games.
"It is not all about Andy, but it is about us trying to perform as a team again on Saturday against Sunderland."
Allardyce hopes Carroll will be able to rejoin the rest of the squad soon enough.
"Andy is improving day by day," he added. "He has started some light training now and we continue to try to monitor it day by day and see when he's going to be available and ready to join back in with the players.
"The very earliest, if we are very lucky, would be the last game before the international break which I think would be Arsenal."
Midfielder Jack Collison, however, remains sidelined by an ongoing knee problem.
"Obviously Jack is a big concern because he has not kicked a ball for us yet since the end of last season," Allardyce added.
"He was a major influence in our promotion year so we would love to get Jack back as quickly as we possibly can."
West Ham battled to a goalless draw at Norwich last weekend, which was their fourth clean sheet of the season, and Allardyce will be looking for more of the same against Sunderland.
"The emphasis of shutting the opposition out has been crucially important for us," he said.
"If I have to be slightly critical, it is about our finishing, which has not been quite as good as it should be to promote the chances we have created.
"But if we work hard to get that clean sheet, then one goal can win us a game."