The former RB Leipzig striker is in line to make his debut in United's Premier League opener against Arsenal this weekend.
Asked about his immediate ambitions, Sesko told MUTV: "Just that we get better, that we connect together, in general, and we, as a team, just try to grow, to grow together step by step because we're getting better.
"We're just even more complete and complete.
"It's just a matter of time when we can fly high again."
On his choice to join United, Sesko continued: "I think, first of all, because of the club.
"It's just a historical club that is unbelievable. For me, the team is great. It is getting better and better and that's why also there is just stuff that makes you come there, gives you this energy that you want to be part of.
"I think it's a great project, in general, and I can't wait to start, definitely.
"I've just been here for a couple of hours," he continued. "And it's already been amazing. I can already feel that we're going to be a great family and it is a pleasure to be part of it.
"It feels good, you know, the thing is it (the badge) fits well and I'm looking forward to just playing in it a lot and try to represent in the good ways possible."