Jodie Taylor scored a hat-trick, while Ellen White, Jordan Nobbs and Toni Duggan were also on target.
The Lionesses, who are fifth in the world rankings, face Spain and Portugal in their remaining group games.
"This team is a work in progress - we're not the finished product yet," said Sampson.
"The exciting part for me is how good we can become over the next five matches. These players enjoy the pressure, they thrive in it and this was the stage they were born to be at.
"With every good performance they put in, it excites me more for how far they can go. We could be the best team in the world."
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Taylor's hat-trick was the first by an England Women player at the finals of a major tournament, and the first any nation has scored at the Women's Euros since 1997.
The Arsenal forward, who was left out of England squads by former boss Hope Powell, had turned down a chance to play for her country in 2010 because she "needed a break" from the game.
The 31-year-old, who scored once at the 2015 World Cup, has had several injuries since joining Arsenal.
"The hat-trick meant a lot to me," she said. "The last two years have been a tough ride. Just to be here fit and healthy is a huge achievement.
"I want to thanks the medics for getting me in a good place, and for Mark for still believing in me and having confidence in me because without that I wouldn't be here."
Sampson added: "Ever since we've known Jodie, I think everyone has known she is a world-class player.
"I've not seen better in the game at anticipating passes in behind, moving into positions to receive the ball.
"Of course, you need the service, but what Jodie has added to her game in the last 12 months in particular is her ability to be an instinctive finisher."
Former England goalkeeper Rachel Brown-Finnis on BBC Radio 5 live:
Jodie Taylor is hungry for success in this wonderful set-up. She spent so long in exile under Hope Powell for whatever reasons, but it spurred her on. It has shaped her as a person.
Former Scotland winger Pat Nevin on BBC Radio 5 live:
Jodie Taylor is one the best and most intelligent movers in the game. Her movement is phenomenal, the timing of it was perfect. She was so calm with the finish.
England can still improve despite thumping arch-rivals Scotland 6-0 in their opening match at Women's Euro 2017, says manager Mark Sampson.