As historic a moment as this was for United, it was a game Solskjaer will want to move on quickly from. It was a slog pretty much from start to finish, Marcus Rashford enduring a frustrating time in front of goal, and while Marcos Rojo will be happy with his night's work, there was little else to write home about. Certainly, the road to the Europa League final in Baku on May 29 is unlikely to feel much closer after this.
Paul Pogba was in the directors' box, and if we told you the jostling among fans to grab a selfie with United's record signing was more of a spectacle than anything out on the pitch, you probably get an idea of just how uninspiring the first half was.
Sure, Rashford and Nemanja Matic were the only survivors from the starting line-up against Leicester and the other nine players on the field were making either their first start or first appearance for the club this season.
In the case of youngsters Angel Gomes and Tahith Chong, this was their first professional start for United, and as the game progressed, it became apparent that the biggest obstacle on the night for Solskjaer's side was likely to be ring rust and a lack of minutes in legs.
Astana's limitations were clear and obvious which, naturally, made the wait for a breakthrough all the more frustrating for a two-thirds full Old Trafford.
Astana got bodies behind the ball and anyone who has watched United in recent times will know they have run into difficulties when sides do that.
United's best chances had fallen to Rashford. There were two in as many minutes, both from excellent balls from the lesser spotted Rojo, the first of which was volleyed wide, the second straight at the goalkeeper.
Fred had forced a diving save from a free kick, having crashed a long-range drive against the woodwork only two minutes in, but it all felt rather forced going forward for United.
This was the first real look at the youngsters in whom Solskjaer is pinning so much faith since the club's off-season tour, when Greenwood, Chong, Gomes and Axel Tuanzebe advanced their claims. It was, though, all about Greenwood in the end.