Rafa Benítez's side faced five of the previous season's top six - Tottenham, Chelsea, Manchester City, Arsenal and Manchester United - in their opening ten games, and had to wait until November, when they beat Watford 1-0, for their first victory.
But United went on to finish 13th and picked up one more point than they had done in 2017/18, when they ended the campaign in tenth.
Next season's fixture list will be announced on the club's official website at 9am (BST) on Thursday and Dummett told nufc.co.uk: "I think everyone looks out for the fixtures.
"You want to know who your first game of the season is against - I think that's the first one you look out for.
"You have that break and then you come back for pre-season excited and ready for the first game of the season, so you always look out for that first game. Hopefully it's a home game, in front of our fans, and we can get off to a good start.
"Last season we had a really tough start so we'll be hoping this season that we don't start off the same way.
"Every game's going to be hard and it's never going to be an easy start no matter who we play, but we just need to aim not to start like we did last season.
"We recovered well after Christmas with the games we won, but we want to try to get this season off to a positive start, and hopefully we can get a couple of wins under our belts early doors."
United have faced Tottenham at home on the opening day for the past two seasons, and haven't began a campaign with three points since 2012 - when, coincidentally, they beat Spurs at St. James' Park with goals from Demba Ba and Hatem Ben Arfa.
But the Magpies have finished strongly in recent reasons, and have won their last game of the season five years in a row: 2-0 against West Ham in 2014/15, 5-1 against Tottenham in 2015/16, 3-0 against Barnsley in 2016/17, 3-0 against Chelsea in 2016/17 and, of course, 4-0 at Fulham just a few weeks ago.
The Magpies' confirmed initial match schedule, including provisional dates and kick-off times, will be revealed on nufc.co.uk at 9am (BST) on Thursday.
