Expectations are probably key to how you view this news.
If you were looking for the club the make an appointment to turn the season around, get us into the top four and competing in CL then you'd definitely be worried by Solskjaer's lack of pedigree.
From my point of view though, I had assumed Mourinho would be here until nearer the summer and had thus accepted that we had zero chance of finishing in the top four or competing in the CL, so this season was already dead to me. As I see it Solskjaer can't have a worse than zero chance of finishing in the top four, so no loss there. But now I can actually look forward to the CL games next year without being certain we're going out in a dismal and depressing manner. As such I'm not particularly bothered if Solskjaer fails to save a season I had already written off. Even the false hope and nostalgia seeing him as manager brings is far more than I was expecting when I woke up this morning.
I say we just relax and try to enjoy the appointment for what it is. Ultimately it only matters if it works.