Paul Hartley's outfit begin their eagerly-awaited return to top-flight action at home to Kilmarnock today, when they'll unfurl the Championship flag after last season's title triumph.
The Taysiders have been busy strengthening their squad during the summer, bringing in 12 summer signings to steel themselves for the step up.
McGowan, one of the many recent arrivals, knows some cynics will still look upon them as candidates to go straight back down but believes his new team are good enough to be challenging for a top-six slot.
McGowan said: "Nobody is too good to go down perhaps with the exception of Celtic. But I look at our squad and think that we have enough to push on and not fight for relegation.
"We will be one of the favourites for relegation. That's normally the case when you come up but I feel we have a team that could push into the top-six.
"We have been really positive all pre-season and have looked great but this is when it really matters.
"What I would say is that I am quietly confident that, if we can reproduce some of the performances we have had in pre-season, we can go on and have a great season."
Dundee's final-day win over Dumbarton at the end of last season means they'll be honoured when the flag is officially raised in front of a crowd expected to exceed 7,000.
And manager Hartley has challenged his players to show they belong in the big-time in the visit of the Ayrshire side.
He said: "The supporters will obviously be looking forward to the unfurling of the flag which is only right.
"But from the players' point of view we'll be thinking only about the game and trying to get off to a positive start."
Dundee striker Phil Roberts begins a four-match suspension and midfielder Kevin McBride is carrying a leg knock, while full-back Gary Irvine has recovered from a groin injury.