The very beginning? How about skipping the flight and all the hassle that comes with airports. Pro tip: Start the time loop when you wake up at the hotel instead.
I don't know if killing Hitler would automatically lead to a better world. What if they had a leader who was not so dumb and attack the soviet union?
It could be like in Stephen Kings 11/22/63 where he prevents the assassination of Kennedy but then the future is much worse.
WW2 was already bound to happen after the treaties of Versailles and Saint-Germain. Hitler also didn't found the NSDAP or invent antisemitism. We of course don't know what would have happened without him, but the near future after WW1 wouldn't have been bright either.