Tammy Abraham proved a handful during his first 60 minutes of global football and man of the match Ruben Loftus-Cheek flourished under the Wembley floodlights, as did fellow debutant Jordan Pickford.
Both Cook and Solanke were part of England Under-20's World Cup triumph in the summer.
The 23-year-old Everton 'keeper's highlights saw him twice deny Timo Werner with sublime low saves in the first half, though his display did not come as a surprise to Southgate.
"I'm really not surprised with what they've done because they've shown that previously in younger ages and in the week in training, there's been an energy about the group".
"Tonight it took him 10 minutes to have a look around and think "Alright okay, I can do this".
Southgate knows the midfielder having played him during his time as England Under-21 manager, and is convinced the Lewisham-born man is capable of operating on the biggest stage.
The first friendly in the build-up to the World Cup in Russian Federation could have been thrown off kilter by the withdrawal of seven players, yet a youthful Three Lions side took their chances to impress against the reigning world champions.
On his side's overall performance, Southgate added: 'We created a couple of really good chances and I felt our use of the ball was excellent throughout the game.
"I felt like I needed to play a lot, so I came in and said I wanted to go away from Chelsea and play games. For me, it was a real positive tonight".
"He's an exciting player - we've got a few exciting players".
The 21-year-old midfielders improve midfield options that Southgate was bemoaning just months ago. I think he'll gain huge confidence from it'.
England have called up Norwich goalkeeper Angus Gunn to replace broken finger victim Jack Butland to their squad for the friendly with Brazil at Wembley on Tuesday.