Steffen netted his three goals in the first 29 minutes as they stormed into a half-time lead, and eventually won 5-0, away against Belarus, in a match played behind closed doors in Serbia, at the start of Group I.
The striker took the place of injured Xherdan Shaqiri and made the most of his opportunity, having scored only once before in 28 international appearances.
Steffen has been at a crossroads in his career over the last season, moving back to Switzerland from after five seasons with VfL Wolfsburg in Germany’s Bundesliga, where he was no longer a regular.
He said his move to Lugano last June had kept alive his chances of staying in the Swiss squad, and he was selected go to the World Cup in Qatar towards the end of 2022, although played only 31 minutes as a substitute against Brazil in a group game.
"I have to play and be fit, otherwise I know that I have no place in the national team. I want to be able to continue playing here as long as I'm fit. I also know that the youngsters will come and at some point my time will be over. The youngsters will then continue to step on the gas. That's why I'll enjoy it as long as I do it still can," he said after his hat trick.
All three were poacher's goals, starting as early as the fourth minute of the game.
“I've certainly scored more difficult goals,” he joked with reporters after the match, having tapped-in twice at the far post and hit home a rebound with his left from close range for the other goal.
“We started a little nervously, also from my side. We were a bit lucky with the crossbar,” he said as Belarus hit the woodwork in the first minute in what turned out to be their only decent effort on the Swiss goal.
“After that we only played for one goal, to win the game, and we deserved to do so. I'm glad that I was able to repay the coach's trust," Steffen added.
