Although Villa are currently focused on trying to earn a first-ever appearance in the Champions League through their Premier League results, their priority at the beginning of the campaign was winning this competition.
Emery has since guided his side through a group featuring Legia Warsaw, AZ Alkmaar and Zrinjski Mostar and knockout fixtures against Ajax and Lille.
One of Villa, Olympiacos, Fiorentina or Club Brugge will now lift the trophy, following on from Roma and West Ham United in 2022 and 2023 respectively.
While Villa are the clear favourites, Emery has a number of selection issues to contend with, including the absence of first-choice goalkeeper Emiliano Martinez.
Martinez suspended, injured for first leg
In the second leg against Lille, Martinez saved two spot kicks in the penalty shootout, but receiving a yellow card - his second of the contest - has led to a one-match ban for Thursday's game.
However, the World Cup winner would not have been available anyway having sustained a hamstring injury against Chelsea on Saturday that also puts his participation in the second leg versus Olympiacos in doubt.
The experienced Olsen will take Martinez's place between the sticks versus the Greek outfit having been required to play the second half versus Chelsea, and Emery has backed the Sweden international to make a positive impact.
Speaking to reporters at a press conference, Emery said: "Martinez is very competitive and very important and helped us a lot. But when an issue like that, the yellow card, and a small injury as well we have to protect, help and support and push another player in the squad.
"Robin Olsen has been very competitive every day in training, when he played he helped the team and the team believes in him and trusts in his performances.
"On Saturday, he played 45 minutes against Chelsea and he saved us. He's a humble man and hopefully he can help us and he can feel comfortable as well playing."
How much football has Olsen played this season?
In his outing against Chelsea, Olsen made a timely intervention to stop Cole Palmer putting Chelsea 3-2 ahead deep into added-on time, a contribution that earned Villa a potentially-decisive share of the spoils.
Aside from that appearance, though, Olsen has made just five starts and one substitute outing for the West Midlands outfit. His only club start since December was in the 4-1 reverse to Manchester City on April 3.
Nevertheless, Olsen did play two times for Sweden during the March international break, starting a 5-2 defeat to Portugal before keeping a clean sheet in a 1-0 triumph over Albania.