Indeed, West Ham travel to Blackburn Rovers in the fifth round of the competition, with Bilic confirming that Randolph will start the cup game - as he has done in previous rounds.
And Bilic insists first-choice goalkeeper Adrian has no issues with the decision.
The Croat told reporters: "Randolph will definitely play. Adrian is fine with that. He is our first keeper but Randolph deserves his chance.
"Every time we have put him in goal he has done brilliantly for us. He is doing the same thing he does when he is playing for Ireland."
Randolph is a clear example of West Ham's strength in depth and that is exactly what holds them in good stead against Blackburn Rovers on Sunday afternoon.
The Hammers need to watch out, of course, as West Brom were thrashed at Reading on Saturday, while Arsenal were held by Hull City.
But Watford demonstrated that a Premier League side can get past Championship opposition if they are patient and resolute.
West Ham won't have home advantage but possess more than enough quality to reach the quarter-finals regardless.