The Magpies face Graham Potter's Seagulls at St. James' Park (kick-off 2pm BST) aiming to win their first opening two top-flight fixtures since 1997 following an impressive 2-0 victory against West Ham United on Saturday.
Along with progressing into the Carabao Cup third round on Tuesday night, courtesy of a 1-0 home win against Blackburn Rovers, Bruce is eager for Newcastle to continue their positive form as their attention returns to league action.
He said: "We all like to get off to a start and we couldn't have had a better week in terms of the results and the players that we brought into the club hitting the ground running like the way they have done.
"We've given ourselves a chance to get off to an outstanding start. Can we get a result against Brighton - a very decent Brighton - who performed very well against Chelsea last week?"
The United boss has no fresh injury concerns, confirming Allan Saint-Maximin will be available to face the Seagulls despite the Frenchman picking up a knock during the latter stages of Tuesday's cup tie against Blackburn.
"It's still a bit too early for (Paul) Dummett, (Matty) Longstaff, (Fabian) Schär and (Martin) Dúbravka," Bruce added. "Everybody else seems to be OK. We got a clean bill of health from the other night which was refreshing. Allan Saint-Maximin is fine.
"We're a lot stronger than what we were. The five lads who have walked through the door have made the squad bigger and better. Certainly, in the evidence of what we've seen over the last couple of weeks, I could say the squad is definitely improving which is what we are wanting to do."
Brighton began their Premier League campaign with a 3-1 defeat against Chelsea on Monday night but Bruce believes Albion will provide a tough test for his side after a spirited display against the Blues.
Last term, both fixtures ended in goalless draws and, with Brighton unbeaten against United in their last six Premier League meetings, Bruce is determined for a better outcome in their opening home meeting of the 2020/21 season.
"They've got a totally different philosophy over the last year or so with Graham (Potter)," the 59-year-old added. "He's came in and changed their style and the way they play. They're all about possession, retaining the ball and they do it very well.
"I was mightily impressed by them against Chelsea. They didn't get the result they maybe warranted but, overall, I thought they did very well so we know what to expect. We know for large parts of the game, they'll have good possession of the ball because that's what they work at all week I presume.
"It's difficult in the Premier League to win a match and draw a game. They weren't exactly classics and much of a spectacle to watch. We hope that we can improve on it and cause them a bigger threat than we did last year.
"It's going to be difficult, they all are, and Brighton have done extremely well against us in the past so we'll have to go out against that."
