McLeish's men will have to upset the number-one ranked side in the world Belgium or World Cup quarter-finalists Russia to qualify automatically for Euro 2020 after being handed a tough draw in Dublin on Sunday.
However, Scotland have already secured the safety net of a Nations League playoff should they fail to secure a place in the top two of Group I by winning their Nations League group, beating Albania twice along the way.
The Albanians won their first ever game at a major tournament two years ago, Northern Ireland made it into the last 16, Iceland, with a population of just over 300,000, shocked England to reach the quarter-finals and Wales upset Belgium to make the semi-finals.
"We'd like to be inspired by smaller countries who went to the Euros last time as third and fourth seeds, like Northern Ireland and Albania," said McLeish. "We want to usurp the teams ranked above us."
Scotland have recent experience of just how hard a time they can expect against Belgium, having been thrashed 4-0 by the World Cup semi-finalists in a friendly at Hampden in September.
"We gifted them it a wee bit, but there was some good elements of our game and we've improved since then," insisted McLeish.
"We have some great teams to play against, long journeys, but I'm confident about the group of players we have."
Belgium boss Roberto Martinez is married to a Scot and recently hired former Scottish international Shaun Maloney as one of his assistants following Thierry Henry's departure to take charge of Monaco.
"I had a disagreement with my daughter when we had to face England (at the World Cup) and now unfortunately it's going to be with my wife, which is always a harder battle to win," Martinez joked.
"Obviously it's going to be a completely different game (to the friendly).
"The Scottish team under Alex McLeish has been developing, winning the Nations League group. Clearly this is a young team that is going to develop."
- 'Little bit cruel' -
Wales' road to repeating their remarkable success at Euro 2016 will see Ryan Giggs's side face World Cup finalists Croatia, as well as Slovakia, Hungary and Azerbaijan in Group E.
Gareth Bale will therefore take on Real Madrid team-mate Luka Modric, who is favourite to win the Ballon d'Or on Monday, but Giggs warned of Croatia's collective strength.
"They've got some outstanding individuals but more than that, they are a team," said Giggs. "A team that never gives up, so we are going to have to match that. It'll be tough, but we are a good team also."
Luck didn't favour Northern Ireland, who were paired with Germany and the Netherlands in Group C alongside Estonia and Belarus.
Draw hosts the Republic of Ireland escaped that group as only two of the 12 nations that will host Euro 2020 could be drawn into the same section with Amsterdam, Dublin and Munich all hosting matches.
"The nature of the draw and how we were moved into that group was a little bit cruel," admitted Northern Ireland manager Michael O'Neill.