You will have to go back 32 years since a marquee Everton signing enjoyed such an outstanding start to his Goodison career as James Rodriguez.
Tony Cottee scored a hat-trick on debut in 1988 following what was then a British record transfer, although with respect that spectacular launch ultimately promised more than his overall career on Merseyside delivered.
Of course, there have been similarly high class introductions since, but rarely does a player so swiftly and expertly justify the thrill and hype accompanying his capture.
If Rodriguez’s first two world class performances are a sign of what is to come, it is no wonder Carlo Ancelotti is so keenly embracing expectations of European qualification.
The highlight of Rodriguez’s Goodison bow - a 5-2 win - would have been his first goal for the club but for the exquisite looped pass in the build-up to Everton’s fourth in the second half, taking out the entire West Bromwich Albion defence. There will not be a more skilful disrobing of a deep backline this season.
“To me it is not a surprise,” said Ancelotti.
“He is able to do this kind of thing. I know his qualities, He is adapting really well and is already comfortable.”
Such was the Colombian’s virtuosity, Dominic Calvert-Lewin’s man-of-the-match status for a hat-trick was not the formality it might have been. He became the youngest English-born Everton player to score a treble since the aforementioned Cottee against Newcastle in 1988.
He will appreciate it was Rodriguez who turned the game, backing up his debut excellence at Tottenham Hotspur last weekend in two especially significant ways within a space of a minute at the end of the first half.
First with a stunner from 20 yards to complete Everton’s recovery from a goal down, and then with the street wisdom to ensure Kieran Gibbs’ stupid shove to the midfielder’s face received the necessary punishment.
Gibbs’ aggression probably did not merit Rodriguez’s exaggerated fall. Nevertheless, it was worthy of the red card instantly shown by referee Mike Dean, the video assistant backing him up.
“Kieran reacted so the referee did not have any other option to give him red,” said West Brom coach Slaven Bilic.
“If he was crafty or savvy after James clipped him, maybe it would have been a yellow for James. The worst option was not to go down and then react with his hand. You can’t complain.”
Bilic took exception to another decision, querying the legality of Everton’s equaliser, scored by Calvert-Lewin having been initially ruled out for offside.
Although the striker was ahead of the opposition defence when flicking in from three yards, the replays showed Seamus Coleman’s cross had ricocheted off defender Darnell Furlong’s back.
Bilic took the objection too far and was promptly dismissed himself, watching the second half from the press box and giving the desk a regular slam in frustration as the ten-men took their punishment.
"As a manager I should be in a situation to ask the referee what’s going on,” he said.
“It’s not like the game was going on, it was half-time - nobody was around. I didn’t swear. I asked him in a frustrated way but I didn’t go over the line. But he just ignored me and gave me red. As a manager you have that right if you are not crossing the line. I told him if you want to kill us, kill us. That’s all.”
Michael Keane’s second goal in a week enabled Everton to overcome another scare after Matheus Pereira equalised with a brilliant 25 yard free-kick early in the second half.
There was enough promise about West Brom with eleven men to lift Bilic’s mood, despite a scoreline which might have been worse but for Lucas Digne striking woodwork. For 45 minutest the Baggies were as enterprising as Leeds United on their visit to Merseyside a week ago, full of pace and energy in attack and prepared to take risks with the ball, while retaining defensive shape with five defenders without it.
Most eye-catching for the visitors was Grady Diangana, the summer signing from West Ham who prompted Mark Noble to take to social media to lament his sale. He showed Noble is a shrewd judge, particularly when dashing through midfield before picking his spot beyond Jordan Pickford on ten minutes.
But when Calvert-Lewin tapped in after Richarlison volleyed Rodriquez’s chipped ball across goal, and added the fifth on 65 minutes, Everton were able to complete the transformation.
That Everton found a way after the early struggle will please Ancelotti as much as last week’s narrow win.
Evolving teams like to measure their improvement by collecting points in those ‘games they would have lost last season’.
In Everton’s case, that phrase can be refined. This is the kind of match they might have lost in most of the last three decades, let alone score five.
Such is the cycle Everton are trying to break, where every few months hope springs, only for the mood to be punctured by unexpected and unnecessary defeat. Not this time.
The hints of a different world with the twinkle-toes of Rodriguez on the pitch and acumen of Ancelotti off it are already obvious.