Slaven Bilic's outfit are set for a showdown at Old Trafford where Jose Mourinho's Manchester United await.
“We shouldn’t really talk too much,” Ayew told his club's official website.
“I think we have the squad, the players and the quality to be able to do something good, but I think a lot of other teams also have great players and great squads, so we need to be calm and work hard.
“We know what we want and the gaffer has given his directions and we are following them.
"It’s only with time and games that you can start to feel what you can do."
Austria forward Marko Arnautovic and Argentina international Pablo Zabaleta are the other big name signings, adding strength to a squad that already boasts of Andy Carroll, Manuel Lanzini and Jose Fonte.
“Last season, I wouldn’t say it was a bad season but we had a lot of ups and downs and we only finished one point away from eighth position," Ayew continued.
"We need to work hard, stay calm and have the belief that we can do something great.”
After scoring five times during the second half of last season, Ayew will hope to lead West Ham's attack, even if a lot more will be expected of hitman Chicharito.