The former Birmingham City manager was named as Gordon Strachan's successor and he will be hoping to get off to a perfect start in the role with a win in this one.
Costa Rica won the only previous meeting between these nations, at the 1990 World Cup, and they are chalked up as a 12/5 (3.40) chance to heap misery upon the Europeans with a win here.
Oli McBurnie of Swansea City and Manchester United's Scott McTominay could make their international debut for Scotland, who will have a new captain after Scott Brown retired from international football.
Low scoring contest?
There have been fewer than three goals scored in six of Costa Rica's last eight matches, but there have been more than two goals scored in just one of Scotland's last eight home fixtures.
Preview and predictions
Scotland will hope to secure a winning start for McLeish but the goals may not flow freely.
Their previous two permanent managers - Craig Levein and Gordon Strachan - both enjoyed 1-0 victories in their respective first fixtures in charge of the national team.
Therefore, it is SportPesa's 33/20 (2.65) quote for fewer than two goals to be scored that may represent best value ahead of Friday's fixture.