Villarreal had just finished fifth in La Liga when they appointed Emery as coach last summer, with the Spaniard's remit to take the club closer to winning titles and securing Champions League qualification.
He could achieve both in one fell swoop in Gdansk, where an upset against the much-fancied United would not only clinch Villarreal their first-ever major trophy but also a place in Europe's premier tournament next season.
Emery knows what it takes to win the Europa League, having triumphed three times in a row with Sevilla between 2014 and 2016, the last time by beating Liverpool 3-1 in the final in Basel. He also reached the final two years ago with Arsenal, only to lose to Chelsea.
"Manchester United were the favourites from the start to win this tournament and they've managed to reach the final," said Emery. "There were other teams who were favourites and haven't done that but we have always seen ourselves as a contender."
Villarreal are also flying the flag for Spain as the one team that denied the English Premier League a clean sweep of European finalists, with Manchester City up against Chelsea in the Champions League final on Saturday.
If Villarreal defeat United, Spain will boast seven of the last 10 Europa League champions, the others belonging to Chelsea in 2013 and 2019, and United in 2017, when Jose Mourinho's side beat Ajax.
"The Premier League is dominating football in Europe," Emery said. "But to reach a final you always have to knock out big teams, or teams that have knocked out big teams themselves, like Dinamo Zagreb. Games like these are a challenge. They tell you what level your team is at."
The Norwegian, now 48, will forever be remembered for his late winner against Bayern Munich in the 1999 Champions League final, and Solskjaer is eager to further embed himself in the club's rich history.
Having helped United secure successive top-four finishes for the first time since Alex Ferguson retired after the last of the club's Premier League titles in 2013, Solskjaer hopes to now end their four-year wait for silverware in Gdansk.
Since replacing Jose Mourinho in December 2018, United's gradual improvement under Solskjaer has resulted in the club finishing sixth, third and, this season, second in the Premier League.
"We've worked together two and a half years now and taken a step into the final after the near-misses we've had. To get to a final is one thing, but when you get to a final you need to win it," said Solskjaer.
"Those nights when you win the trophy it brings everyone together, it's a celebration.
"When we won in '99 it didn't make me a better player. It didn't make us individually better players, but as a group we believed that we could go on to win more stuff and we comfortably won the league the next couple of seasons."
Only three starters from the 2-0 win over Ajax in the 2017 final remain at the club -- Paul Pogba, Marcus Rashford and Juan Mata -- with United seeking to end their longest run without a trophy since the 1980s.
"This game's important for us. We're so close to being a team that can compete and win trophies every single season. Maybe winning this title, this Europa League, can give us that little push that we need," said Rashford.
Solskjaer will give captain Harry Maguire until Tuesday's final training session to prove his fitness, although the England defender is highly unlikely to play after damaging ankle ligaments two weeks ago.
Another obstacle in United's way is Unai Emery, a three-time Europa League champion with Sevilla who has overseen a 14-match unbeaten run in Europe with Villarreal to reach his fifth final.
All four previous meetings between United and Villarreal have finished goalless. A similar outcome is entirely plausible in Poland, but this time there will be a winner and loser regardless.
"It's going to be special. You've got to be proud to be able to lead a Manchester United team out to a final," said Solskjaer.
"It's been a fantastic journey and, as we say in Norwegian, veien er målet (the goal is the journey). This is just a step on the road to bringing our Man United back."