The defender failed to make a single league appearance in a year at Chelsea before moving to the Stadium of Light this summer.
Djilobodji became Moyes' first signing as Black Cats manager when the Scot paid £8 million to sign the defender from Chelsea earlier this summer.
The 27-year-old is yet to taste any Premier League action despite first arriving in England a year ago, with his only first-team appearance for the Blues coming as a last-minute substitute in the EFL Cup before he moved to Bundesliga side Werder Bremen on loan.
However, the Senegal defender looks set to be given a baptism of fire on Sunday as he gets set to start for Moyes' side against newly-promoted local rivals Middlesbrough after Younes Kaboul's move to Watford.
Though a player with such a lack of English top-flight experience starting in such a highly-charged game may be a concern for supporters, Moyes insists there is no need to worry about the defender.
He said, via the Chronicle: "I got Papy with the intention of needing another centre-half and a left-footed one so if anything did happen to Younes, Papy was available.
"I see Papy as being a naturally left-footed centre-half. That’s what I am looking to build from. I would have preferred him to have a month or two to get to know him a bit better, to get more coaching work into him.
"But he played the second half of the Bundesliga season at Werder Bremen, and played very well, so this should not be too big a shock for him."
Sunderland will be desperate to get their home campaign off to a perfect start against Boro after suffering a late 2-1 defeat to Manchester City in their season opener last weekend.