As international breaks go, the one England have just enjoyed was quite eventful, even if nothing Gareth Southgate’s players could produce on the pitch was likely to steal the headlines from the way in which Wayne Rooney celebrated a rare weekend off.

How assiduously Rooney can put the past behind him and resume what was shaping up to be a promising return to his former club will be one of the focal points when Premier League football returns at the weekend, as will the behaviour of Dele Alli. A theory is emerging that the Tottenham player has not just taken Rooney’s place in the England team but also appropriated his penchant for needless controversy, and both forwards will be in the spotlight when Spurs visit Goodison on Saturday.

Other sources of scrutiny, whether they play or not, will be Alexis Sánchez for Arsenal, Philippe Coutinho for Liverpool, Virgil van Dijk for Southampton and Riyad Mahrez for Leicester, all players who might have hoped or been led to believe they would be turning out for someone else by now. Then there is the question of how Manchester City will perform against Liverpool, now Sergio Agüero and Raheem Sterling know they are not quite the last word in attacking threats as far as Pep Guardiola is concerned, not forgetting the issue over whether Alex Oxlade-Chamberlain is going to look any more a £40m player than he did in his last couple of outings for Arsenal and England.

Pressure all around then, though in terms of teams rather than individuals there is no doubt who will be going into the weekend with the most fear and dread. Three games into the new season – back in days of yore this would be the stage when the first league tables would start to be published – there are still three teams awaiting their first point. Crystal Palace are actually still awaiting their first goal, though the two sides bookending the Eagles in the bottom three are not doing much better. Bournemouth have one, Charlie Daniels’ splendid though misleading early strike against Manchester City at the end of last month, and while West Ham have scored twice they have already conceded 10 and as a result sit at the foot of the table with the worst goal difference in the division.

As might be expected, the managerial futures of Frank de Boer and Slaven Bilic have been called into question, though Eddie Howe is probably in credit for a little while longer. Interestingly Bilic at West Ham is considered a tactical dunce, hence the popular theory that Rafael Benítez would make a suitable replacement, while De Boer has been accused of trying to introduce too much of a tactical rethink too soon. You can tell how badly that has gone down by the number of Palace fans now coming round to the idea that Roy Hodgson might be an improvement.

For Palace and West Ham at least, this weekend could be make or break. Howe takes his Bournemouth side to Arsenal, where in normal circumstances they will be allowed to play football, and might even be able to take advantage of any non-normal discontent within the Gunners’ ranks. Bournemouth lost the corresponding fixture 3-1 last season, though Sánchez scored two of the Arsenal goals. While Bournemouth will have to show more urgency and conviction than they have summoned thus far this season to achieve an upset, even if they lose it ought not to be viewed too damningly. The Emirates is still a difficult place to go in search of a win, particularly for a club the size of Bournemouth, and it would be harsh for anyone to reach for the panic button as a result of a defeat at Arsenal.

Palace and West Ham, on the other hand, have no such margin for error. Both are faced with ostensibly winnable games, Palace at Burnley on Sunday and West Ham at home to Huddersfield on Monday, yet as everyone knows, the term “winnable game” is often stretched to the point of meaninglessness in the Premier League. There is hope for Palace at Turf Moor, though Burnley’s home form was what kept them up last season they are still searching for their first win in front of their own fans this time after going down to West Brom last month. But Burnley won home and away against Palace last season and are always confident under Sean Dyche. They have made a convincing start to this campaign – winning at Chelsea and drawing with Spurs at Wembley no less – and after strengthening their front line in summer may be looking at something a little more rewarding than the usual relegation battle.

The same could be said of Huddersfield, who have made even more of a flying start than Burnley thanks to that 3-0 opening day win at Selhurst Park. It is true that the Terriers have yet to play any of the biggest teams – their seven points to date came courtesy of Palace, Newcastle and Southampton – though unlike West Ham’s sieve-like defence they have impressed in recording three clean sheets. Manchester United are the only Premier League side who can make the same boast, and though a visit from Huddersfield must have looked like three points in the bag when the fixtures were first published, West Ham fans are now looking a long way up the table at their next opponents.

Time up already? Frank de Boer may not survive if Palace suffer a fourth successive defeat in their match at Burnley on Sunday. Photograph: Jason Hearn/Action Plus via Getty Images

Yet while “winnable” might not be the correct expression to apply to Palace and West Ham’s upcoming fixtures against smallish but buoyant sides, the hierarchies at the two London clubs are still likely to regard them as “unlosable”. If you are in a relegation struggle after just three games, what does it say if you cannot beat Huddersfield at home or Burnley away? It is probably time for action on the managerial front, before the games against the Premier League’s big boys come along. Harsh but defensible.

It is a results game after all, as hundreds of managers on the verge of the sack have pointed out. There is no time for sentiment or patience if things are not working out on the pitch. Everyone knows the bottom line here, but three Premier League managers go into the weekend feeling it more than most. The simple rule is not so much three strikes and you are out – though De Boer in particular seems to have come close – but three blanks put an incredible amount of pressure on the fourth attempt, as does the knowledge that the sequence will most likely be brought to an end before a fifth.