They are sixth in the table ahead of Sunday's trip to Leicester City, and Solskjaer said they were ahead of schedule in terms of being able to secure a top four finish and Champions League football for next season.
"We've had now six weeks together. We've found out what strengths, weaknesses we've got," he told his weekly news conference.
"I think we've risen to most of the challenges... maybe they will make us move to the next level because I think we've given ourselves a chance now to get into the top four maybe earlier than we thought."
After facing Leicester, United travel to struggling Fulham before hosting Paris St Germain in the Champions League last 16 and then visiting Chelsea in the FA Cup fifth round later in February.
Solskjaer's men then welcome league leaders Liverpool to Old Trafford and close out the month by coming back to London to take on Crystal Palace in the Premier League.
"It's not too many games... but it's tough opposition," he added. "You start with this game against Leicester, Fulham away as well is also a tough one.
"Then you've got the three big ones you can call it, with PSG, Chelsea and Liverpool after each other. Then a very hard one, when you think you've done with those three, with Palace away. So it's a tough month - but we're ready.
"I've got a big squad, it's only Marcos Rojo now who's out for a period, the rest are fit and available."
(Reporting by Simon Jennings in Bengaluru; Editing by Ken Ferris)
