On April 6 of last season, with the Premier League heading towards its climax, Arsenal travelled to Goodison Park for a battle that, while not a determinant of the outcome, would go a long way to defining the race for the all-important fourth Champions League position.
And Everton were brilliant, leading 3-0 after an hour with the Gunners simply unable to cope. With six games of their campaign to go, Roberto Martinez's side had a top-four spot in their grasp.
In the end, however, they just couldn't quite last the distance. Three defeats followed, and all they could manage was fifth. Arsenal won their final five and, doing what they always eventually do, qualified for the Champions League.
You felt that last season was a real chance to take advantage of the madness going on around them and nick a place that would usually be out of their reach.
But they came up just short.
That is not at all to say their season was a failure. A club the size of Everton have no divine right to be in, or even within reach, of the top four. As much a case could be made for them earning fifth as much as losing fourth—especially considering the stature of a couple of the clubs they finished above.
But it was a chance all the same.
Arsenal have gone big this summer to make sure there are no more potential slip-ups, and Tottenham have hired a proper manager in Mauricio Pochettino, who will surely help them push on.
Then there's Manchester United and Louis van Gaal.
There is no doubting Dutchman is a terrific manager—although maybe not quite the demigod he has been made out to be by some since the World Cup—but he will make Manchester United better.
Admittedly, they could hardly get worse.
Whichever way you look at it, Everton's major transfer business so far this summer is yet to elevate them into a stronger position.
There is still time. We are, of course, in the farcical period where the season has begun (in a post-Community Shield sense), but the transfer window has yet to close. A few more faces will still be ushered through the door of Goodison Park.
But considering the £28 million outlay on Lukaku, a fee that nearly doubled their previous transfer record, it is hard to imagine that there is a significant amount left in the coffers of the famously cash-strapped club.
Club chairman Bill Kenwright wants success, but he won't let Everton fall into financial disrepair as a result. Leeds United gambled on that a few years back, and they lost 2-0 to Millwall the weekend just gone.
And there is also the Europa League (or to give it it's official name, "The Much-Derided Europa League") to contend with.
Despite its reputation as an occasionally unwelcome irritant to some, it shouldn't be forgotten that Everton have been absent from the continental game since 2010. European football should always be viewed as a platform and an opportunity.
For Martinez, though, the squad depth to cope with it will be a concern despite the fact that they have two less games to play between now and Christmas than if they'd qualified for the Champions League. Everton possess quality but not quantity. The journeys, distances and Thursday-to-Sunday nature of the competition will also be a worrying factor.
Last season, Everton were a joy to watch for most of the season, and we can only hope for more of the same again this time round.
Unfortunately, though, the top four will once again prove a step too far for Martinez and his side.