Carlo Ancelotti’s side still sit top of the Premier League table on goal difference, having amassed 13 points from their first six games, including four successive wins to start the season followed by a hard-fought derby draw.
Plus, they’ve booked their place in December’s EFL Cup quarter-finals, too, and with a tie at home to Manchester United to look forward to, the Blues should fancy their chances of progressing further yet.
But how does Everton’s start to this season compare to previous great beginnings? And how did those seasons pan out for the men in royal blue?
2016-17: Koeman gets off to a flyer
After 6 games: 13 points, 2nd place At end of season: 61 points, 7th place
Ronald Koeman’s first full season at Everton started with the exact same record as Carlo Ancelotti’s - four wins (all in succession), a draw and a defeat.
After replacing the sacked Roberto Martinez after two consecutive 11th-placed finishes, the Dutchman looked to have Everton back on the right track, following up a solid opening-draw with Spurs by beating West Brom, Stoke, Sunderland and Middlesbrough in a row.
Romelu Lukaku was scoring goals for fun and new signing Idrissa Gueye was providing some much-needed midfield still, but a defeat to Bournemouth in their sixth league game marked the start of a wretched run, which saw the Toffees win just one in ten matches.
Everton recovered after Christmas to salvage a seventh-placed finish and Europa League football, but an abysmal start to the following season saw Koeman sacked by October.
2012-13: Moyes’ final season starts in style
After 6 games: 13 points, 2nd place At end of season: 63 points, 6th place
David Moyes amassed the same points haul as Koeman and Ancelotti, including in what proved to be his final campaign at Everton before replacing Sir Alex Ferguson at Manchester United.
And Moyes beat his eventual predecessor on the opening day to set the tone for an impressive season, followed up by a stunning 3-1 win at Aston Villa.
The Blues briefly dipped by losing at West Brom and conceding an injury-time equaliser against Newcastle just moments after regaining the lead, but successive wins over Swansea and Southampton meant only Chelsea sat above them after six games.
But that sixth game of the season was followed by four consecutive draws, which rather told the story of a campaign which felt a missed opportunity for Moyes.
They also missed out on Europe after both domestic cups were won by sides below them in Swansea and Roberto Martinez’s Wigan.
2004-05: Passports at the ready...
After 6 games: 13 points, 3rd place At end of season: 61 points, 4th place
But the first time Moyes managed 13 points from his opening six games will live longer in the memory, as the platform from which Everton went on to record their highest finish in Premier League history.
After finishing 17th in 2003-04 and losing Wayne Rooney to Manchester Utd, hopes were hardly sky-high for Moyes’ third full term at the helm, and that was compounded by the opening day 4-1 home defeat to champions Arsenal.
But seven wins from their next nine league games followed for Everton - six of which by a one-goal margin - as they eventually went on to finish fourth and qualify for the Champions League (less said about that, the better, though).
Their eventual points total of 61 remains the second-lowest in Premier League history to qualify for Europe’s elite competition - only Liverpool with 60 the previous year edge them out in that regard.
2013-14: Martinez makes strong first impression
After 6 games: 12 points, 4th place At end of season: 72 points, 5th place
You wouldn’t have banked on Roberto Martinez’s first season at Everton making this top five after the first three games, which comprised a 2-2 stalemate with Norwich and goalless draws with Cardiff and West Brom.
But reinvigorated by deadline-day arrivals Romelu Lukaku, Gareth Barry and James McCarthy, the Blues then found their feet. Jose Mourinho’s Chelsea were the first side beaten by Martinez’s Everton, then West Ham (courtesy of not one, but two Leighton Baines free-kicks), then Alan Pardew’s Newcastle. Soon enough, Everton were fourth.
And they were there or thereabouts for the remainder of the season, only stumbling at the final few hurdles to miss out on Champions League qualification to Arsenal after seven straight wins between March and April.
Their points total of 72 yielded a fifth-placed finish, remarkably 11 better than the year Everton took fourth, and remains Everton’s best in a Premier League season.
2006-07: Johnson gets Everton firing again
After 6 games: 12 points, 4th place At end of season: 58 points, 6th place
Only Everton could follow up a 3-0 home win over Liverpool with a 2-2 draw at Goodison Park to Wigan Athletic, a side who only survived that season due to having a goal difference superior by one to that of Sheffield United.
Still, that was one of few grumbles from a largely enjoyable season under Moyes, which saw Everton go the first seven matches unbeaten, record that euphoric derby win, and find a new talisman in summer signing Andrew Johnson.
After finishing 11th the previous year, this campaign represented huge strides forward, and great potential in the likes of Joleon Lescott in defence, Mikel Arteta as the midfield maestro, and Johnson supplying the bulk of the goals.
Only a final-day draw at Chelsea stopped Everton finishing fifth, though sixth was still enough to secure what proved to be a memorable UEFA Cup journey the following season.