The newly-promoted Canaries have so far proved that they will not be relegation fodder in the top flight, though, and will be hopeful of returning to winning ways in their last outing before the international break.
West Ham hopes were high heading into the new season following a summer in which they spent more than £70m, but fans may have been fearing another frustrating campaign following their opening-day thrashing at the hands of Manchester City.
Things have since improved for the Irons, though, and they go into Saturday's match looking for a third win in a row following their 3-1 triumph over Watford last weekend and an EFL Cup victory at Newport County.
There was more than just the scoreline to celebrate as Manuel Pellegrini's side picked up their first Premier League win of the season at Vicarage Road, with record signing Sebastien Haller opening his account with a match-winning brace.
The Hammers now face back-to-back matches against newly-promoted opposition - Aston Villa are next up after the international break - and will see that as a good opportunity to continue their winning run having made such a slow start to last season.
To do so, they will have to get back to winning ways at home having only picked up maximum points in one of their last four league outings at the London Stadium, while they could lose consecutive matches in front of their own fans for the first time in almost a year.
Norwich will certainly feel as though they are capable of pulling off an upset, having pushed Chelsea all the way last weekend and caused Liverpool numerous problems despite their heavy defeat on the opening day.
The Pukki party is in full swing following his record-equalling five goals from his opening three games in the division, while Norwich as a team have earned praise for their refusal to change from their attacking philosophy.
Only Liverpool and Manchester City have scored more goals than Norwich in the early stages of the campaign - and only three teams have scored more than Pukki alone, for that matter - but the Canaries also have the worst defensive record after three games.
Pukki has more goals than Norwich have points this term and manager Daniel Farke will know that it is points - not plaudits - which keep a team in the division.
Norwich must also bounce back from a humiliating 1-0 defeat at League Two Crawley Town in the second round round of the EFL Cup on Tuesday, although Farke did make numerous changes for that match.
West Ham form: LDWW
Norwich form: LWLL
Michail Antonio limped off after only eight minutes of the EFL Cup win over Newport due to a thigh injury and, while the severity of the injury is yet to be confirmed, he is expected to miss this weekend's match as a result.
Pellegrini can welcome Javier Hernandez back into the fold following a knee injury, although the Mexican striker is unlikely to usurp Haller in the starting lineup following his brace last weekend.
There promises to be competition for places in midfield, though, with fit-again captain Mark Noble expected to hold on to his spot despite Jack Wilshere scoring his first goal for the club in the EFL Cup.
In addition to losing the match, Norwich also lost Timm Klose to another injury having only just seen him return, and the centre-back now faces more time on the sidelines.
There could be better news in the shape of Josip Drmic, though, as the Swiss forward nears a return from a hamstring strain.
West Ham possible starting lineup:
Fabianski; Fredericks, Diop, Ogbonna, Masuaku; Rice, Noble; Yarmolenko, Lanzini, Anderson; Haller
Norwich possible starting lineup:
Krul; Aarons, Hanley, Godfrey, Lewis; Leitner, Trybull; Buendia, Stiepermann, Cantwell; Pukki
We say: West Ham 2-2 Norwich
These two sides both have goals in them - at either end. If Norwich perform as they have in their three matches so far then they should be able to breach the West Ham defence, perhaps more than once, but you would also not rule out the hosts doing exactly the same. We're going for an entertaining score draw.
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