England's Nations League exploits mean they are already assured of at least a play-off spot, as they finished top of their group ahead of Spain and Croatia, while they also impressed at the World Cup earlier this year.
The country have captured the imagination of supporters for an entertaining brand of football and Southgate's trust in young players, though the manager has told his players to start experiencing the pressure of expectation.
"We're favourites and that's something we've got to start getting used to anyway," Southgate told reporters.
"We're going to have high expectations over the next few years and adapting to that is probably key to our development as a team. Look, it's up to us, isn't it?
"I think it can be a really exciting 18 months. We've got this coming summer to look forward to and then a big chance because we host [some games at Euro 2020] and we have to make sure we are there.
"That could be an incredibly exciting two-year period from the World Cup right through and a great opportunity for our players."
The two semi-finals will take place on the June 5-6, before the third-place play-off and a final on June 9.
England are not scheduled to play another match until March, when they will begin their Euro 2020 qualifying campaign with matches against Czech Republic and Montenegro.