For Manchester United, it is difficult to see how their first game of the new season could have gone much better other than perhaps another goal or two to polish up their superiority. As it was, they shouldn’t be too greedy. Romelu Lukaku has wasted little time demonstrating why he became the club’s most expensive summer recruit and, on this evidence, it is shaping up to be a season of rich promise for José≈ Mourinho’s team.

Lukaku should certainly have dispelled any lingering self-doubt with the two goals that laid the foundations for the most emphatic league win of the Mourinho era. Not that the £75m signing displayed even a flicker of stage fright with the left-foot finish and close-range header with which he introduced himself to the Old Trafford crowd.

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Lukaku ended a hugely satisfying afternoon waving appreciatively to the Stretford End and he might have finished with the ball as a souvenir had it not been for a brilliant saving tackle by Pablo Zabaleta, one of three West Ham debutants, to deny him a hat-trick just after the hour.

Yet this was more than just a story of Lukaku easing into life in Manchester and, though the new signing deserves the headlines, the form of Marcus Rashford and Paul Pogba, among others, should also fill Mourinho with optimism that his team are capable of significant improvement after last season’s sixth-placed finish.

Potential champions? You wouldn’t bet your mortgage against it and, for what it is worth at this time of the season, this rout puts them top already. Mourinho also made the point afterwards that we should anticipate the team getting better. “I’m not going to say the performance was perfect because it wasn’t perfect. There is still room for improvement.”

Henrikh Mkhitaryan was another of the star performers and, not for the first time, it felt faintly ludicrous that Chelsea had allowed Nemanja Matic to defect to one of their title rivals. Matic fitted in seamlessly and the home side were not flattered by the late one-two when the substitute Anthony Martial slotted in the third goal, quickly followed by the brilliantly effective Pogba knocking another in from 20 yards. It was a tepid show from West Ham and they have now lost 11 opening-day fixtures in the Premier League era, more than any other club.

As the crowd serenaded Mourinho and Joe Hart, West Ham’s new goalkeeper, was reminded that it was a long way down since he was winning championships with Manchester City, it did not seem to matter too much that Victor Lindelof, the £31m acquisition from Benfica, was not even in the home squad because of his unimpressive form in pre-season.

Another manager might have felt duty-bound to involve such a costly signing. Mourinho does not operate with those kinds of constraints and Phil Jones was recalled alongside Eric Bailly to make sure Javier Hernández did not have a profitable return to Old Trafford.

Hernández scored 37 goals in 103 league games during his days in Manchester and one imagines he would have loved the kind of chances that Lukaku’s team-mates served up for the Belgian. Mkhitaryan’s expertly delivered free-kick for the second goal was the case in point. Rashford’s beautifully weighted pass for the first was another. These are the opportunities Lukaku thrives upon and, as long as it continues this way, he should get a hatful this season. Rashford was also involved in the second goal, having been chopped down by Zabaleta for the free-kick, and the teenager curled another shot against the post before Martial took over for the last 10 minutes.

These are early days but Mourinho, slowly but surely, seems to be assembling a side with no obvious weaknesses and Matic’s contribution for the first goal was a splendid snapshot of why he had been added to the payroll. Matic played with great control and it was his interception, cutting out Pedro Obiang’s pass, that sent Rashford haring away on the counter-attacking move that led to Lukaku scoring from 12 yards.

West Ham had defended stoutly until that point but they set about the afternoon with a distinct lack of adventure and there were only sporadic moments when their new-look frontline of Hernández, Marko Arnautovic and André Ayew flickered into life. Arnautovic had their best moment with a looping header that David de Gea tipped over the crossbar but the score was 2-0 at that stage and, for the most part, Slaven Bilic’s men were pinned inside their own half. “They were better than us in every department,” Bilic reflected. “We are very low.”

Mkhitaryan’s precise pass left Martial with the opportunity to stroke in the third goal and the away end was rapidly emptying as Pogba added the final flourish and Hart was beaten for the second time in three minutes. “The fans have reason to be optimistic,” Mourinho said.