Bilic brought in some top players - such as Dimitri Payet, Victor Moses, Pedro Obiang and Angelo Ogbonna - while Andy Carroll has returned to full fitness.
Many pundits said swapping a safe pair of hands like Allardyce for a manager who was untested in the Premier League was a big risk.
If it was a gamble, it already looks to be paying off for Gold and Sullivan.
The former Croatia boss has masterminded a hat-trick of away wins over Arsenal, Liverpool and Manchester City, as well as a home win over Newcastle United to seal West Ham's best start to a season for seven years.
'Who knows what could happen this season'
And despite going out of the Capital One Cup to Leicester City 2-1 on Tuesday night, Gold has told the club's official website they are set for a memorable season.
"At the start we said our aim was to finish in the top 10, but who knows what could happen now this season," Gold told whufc.com.
"(We) beat Liverpool, Newcastle and the Premier League leaders last weekend and now have three wins from the last three (Premier League) games.
"We need to avoid any serious long-term injuries and if we manage to do that I think this could be a very special season."
Ham-strung by injuries
West Ham's recent history is littered with tales of seasons being jeopardised by long-term injuries to key players.
The Hammers finally seemed to have a good thing going on under Alan Curbishley, with first Carlos Tevez and then Craig Bellamy and Dean Ashton on the books at one stage.
But pairings of Ashton and Tevez or Ashton and Bellamy would never come to fruition to see if they could strike up the deadly partnership many predicted.
That was because both Ashton and Bellamy spent long spells out through injury - Ashton's so bad he was eventually forced to retire aged just 26.
Keiron Dyer was also part of that squad but barely featured for the Hammers, making just 30 appearances - many as sub - over four injury-ravaged years.
Can Bilic keep Carroll fit and focused?
Most recently fans have had to endure another injury saga as Andy Carroll battles to resurrect his once-promising career at Upton Park.
In the two-and-a-half years since making his move to Upton Park permanent for a club record fee on a six-year deal, Carroll has made just 28 appearances, scoring seven goals.
His latest return from a long absence came with a start against Leicester City on Tuesday night, where he looked rusty and ineffectual.
The key will be keeping him fit and interested, though, if, as is expected, he plays second fiddle to main striker Diafra Sakho.
If Bilic can do that and keep West Ham's other key players fit and firing, Gold may well be right.