The East Londoners have proved they can be a match for anyone on their day on more than one occasion this season.
Bilic's freeflowing side have already beaten Arsenal, Manchester City and Liverpool away as well as Chelsea at home before completing a historic double over the Anfield side.
Is it a glorious omen?
That's because the last time they did the double over Liverpool was 52 years ago in the 1963/64 season - which any Hammers fan worth their salt will know was the season they won their first ever FA Cup.
Liverpool won the title that season but the Hammers had their number beating them home and away.
That season too, West Ham proved they could match anyone on their day and showed their pedigree in the FA Cup where they beat London rivals Charlton Athletic 3-0, eventually saw off near neighbours Leyton Orient by the same score in a fourth round replay, scored another three in a 3-1 win over Swindon, matched that score against Burnley and then incredibly produced the same 3-1 scoreline against Manchester United in the semi-final to set up a final against Preston North End.
That famous day they would score three again as they triumphed 3-2 with goals from John Sissons, Geoff Hurst and Ronnie Boyce.
Could it be their destiny 52 years on?
Could it be fate that the Hammers will go on to crown their last ever season at their beloved Boleyn Ground home of 112 years by lifting the FA Cup for a fourth time.
It would certainly be ironic given Liverpool stopped the Hammers ending their trophy drought in that epic FA Cup final back in 2006.
West Ham will move to the 54,000 seater Olympic Stadium in the summer, one of the finest football arenas in Europe. And European football would come as a result of an FA Cup win and would have a fitting stage.
Do Hammers fans dare to dream further still, though? Because what happened the season after their 1964 FA Cup victory?
The club's finest moment, winning the 1965 European Cup Winners' Cup.
Maybe fortune will come out of hiding after 36 years without a major trophy. The journey begins against Championship side Wolverhampton Wanderers