Bilic's side are the second-highest scorers in the top-flight behind leaders Manchester City and boast the best away record, too, with four wins and a draw taken from their five games on the road so far.
But it is who the East Londoners have beaten on their travels, and the manner of the victories, which has had everyone tipping them for big things.
The Hammers started the season with a comfortable 2-0 win over Arsenal at the Emirates before going on to thrash Liverpool 3-0 at Anfield, see off City 2-1 at the Etihad and most recently beat in-form Crystal Palace 3-1 last time out.
Bilic's attacking style and some fantastic transfer business over the summer seems to have lifted West Ham onto another level this season.
Star players like Dimitri Payet, Manuel Lanzini and Victor Moses have turned West Ham into a genuine threat.
Now fans and pundits are predicting a bright future, with the move to the 54,000 seater Olympic Stadium looming next season.
'They can challenge'
And speaking on talkSPORT, Hammers legend Martin, who watches a lot of football in his role as a pundit for the radio station, said he believes his old side can upset the odds and challenge the Premier League elite for a place at Europe's top table
"I think they can (stay in the Champions League spots)," Martin told talkSPORT.
"Listen, I know it's still early days, but I really do believe they've got a lot of very good players at West Ham now and if they can keep all those players fit they can challenge.
"I've spoken to the players there and they're really enjoying playing under Bilic, it's looking very good for them."
High praise but a big ask
Martin knows a decent West Ham side when he sees one.
He played in what is regarded as the best Hammers side in recent memory, the Boys of '86, who came so close to winning the league before finishing third under John Lyall.
But West Ham would need to maintain their current average of nearly two points per game if they are to make the Champions League, so it is a tough ask.
And Bilic will need to rectify their indifferent home form if they are to do that, with the Hammers having lost to Leicester City and Bournemouth and drawn with Norwich City at Upton Park.
Out of sorts Chelsea are in town next, in what is West Ham's sternest test of the season at home so far.
A win for the Hammers would leave them on 20 points from the first 10 games. Do that and Martin's prediction does not seem so far fetched.