Saints are one of five clubs on maximum points after two games and, as the only one of those sides in action on Tuesday, they know victory would take them to the top of the table outright.
Last season was notable for the success of the promoted clubs, with Norwich going straight up to the Premier League while Leeds and Millwall challenged for play-off spots for most of the season.
Connolly has scored in both of Southampton's wins over Leeds and Barnsley, and he told the club's official website: "It's only two games in, so there's a long way to go.
"We've hit the ground running, but it's a long, long season and everyone has got points to prove, so let's hope it stays like that and we'll see where we are at the end of the season."
Connolly is preparing for a tough test against Paul Jewell's men on Tuesday, and the opposition boss will certainly know what to expect from the striker.
"It's another tough game, but a lovely place to go, a great footballing club and stadium with a nice pitch, and I'm sure all of the lads are looking forward to it," added Connolly.
"I don't know how they're playing at the minute, but I know Paul Jewell, who signed me at Wigan. He's a very good manager, and I know his sides will make it a very tough game, but they will be expecting the same, so it should be good.
"I'm in as good a shape as I've ever been in and I've averaged nearly a goal a game in this league before. I've won this division before, so it's no problem for me, and I look forward to every game."