The Hammers fell to a 2-0 loss at home to Newcastle United in their opening game of the campaign, while Charlton kicked off their League One season with victory at Crewe Alexandra.
West Ham have been bottom of the Premier League after the opening round of fixtures in the last three seasons following heavy defeats to Manchester City (twice) and Liverpool.
Saturday night's two-goal loss against Newcastle may not have been as bad as those previous defeats, but it is clear that David Moyes has a lot of work to do this season.
United do not have the best of recent records in the EFL Cup, though, exiting in rounds four and three to Tottenham Hotspur and Oxford United respectively in the last two seasons.
The 4-0 loss to Oxford 12 months ago is a result that is still fresh in West Ham fans' minds, with Manuel Pellegrini coming in for plenty of criticism after that heavy defeat.
Coincidentally, Charlton were 4-0 winners the last time they faced West Ham in any competition, with that victory coming in the Premier League 13 years ago.
Athletic have fallen a long way since those heady days and now find themselves back in the third tier following last season's relegation from the Championship.
They have started the new season brightly, however, thanks to a 3-1 win at Swindon Town in round one of the EFL Cup, followed by a 2-1 win at Crewe in their opening league game.
Lee Bowyer's men have reached the third round of this competition in just one of the last 12 seasons, though, most recently being knocked out by Forest Green Rovers in round one.
Earning promotion back to the Championship will be Bowyer's main goal this term, but a cup run is always welcome and this could prove to be another tricky tie for West Ham.
West Ham form (all competitions): L
Charlton Athletic EFL Cup form: W
Charlton Athletic form (all competitions): WW
Given the quick turnaround in matches, with a trip to Arsenal to come next weekend, Moyes will likely heavily rotate his squad for this cup tie.
Charlton's squad depth is not quite so vast, of course, but Bowyer will still likely make some changes for this short trip to the London Stadium.
Promising youngster Dylan Levitt was brought in on loan from Manchester United last week and seems certain to be given some minutes here.
Jonathan Williams was used as a second-half substitute in the win over Crewe and, fitness depending, is in contention to return to the XI in midweek.
West Ham possible starting lineup:
Randolph; Johnson, Balbuena, Cardoso, Masuaku; Coventry, Cullen; Anderson, Lanzini, Holland; Haller
Charlton possible starting lineup:
Amos; Lapslie, Pratley, Oshilaja, Purrington; Levitt, Forster-Caskey; Oztumer, Williams, Doughty; Bonne
We say: West Ham United 2-1 Charlton Athletic
West Ham are likely to field a weakened XI here and, given the way Charlton have started the 2020-21 campaign, an upset is definitely on the cards. However, the Hammers have won all three previous meetings with Athletic in this competition and should still have enough quality to get the job done on home soil.