The British driver sits third in the standings after claiming a fourth, a third and a fifth in the first three races, with the consistent pace being shown in both qualifying and the race contributing to his significant 21-point lead over team-mate Daniel Ricciardo.
Asked ahead of this weekend's Spanish Grand Prix if the team was concerned about failing to continue its impressive run, Norris replied: "No, we are still always confident and looking ahead to being better and trying to beat the Red Bulls or the Mercedes in qualifying or the races.
"I still go for those opportunities, it is not like I hang on to what I have got so we are still trying to achieve as much as possible.
"I think it is just being realistic at the same time. It is the mix of confidence and being realistic. I know sometimes it can go wrong and we don't look as great as we are."
After finishing third in last season's constructors' championship, nearest rivals Aston Martin and Alpine have seemingly taken a step backwards, with Ferrari emerging as the closest contender for best of the rest.
Whilst Norris acknowledged McLaren's superiority to commence the campaign, he warned the tables can quickly turn.
"Things have gone very well for us, I feel like I am doing a good job in qualifying and putting myself where I need to," he added.
"Maybe not so much at Imola or Portugal in Q3 run two but everything apart from that has gone well.
"The races as well, the restarts and the launches, a lot of things are going well but it is just as easy for it to go not so well.
"I want to continue what we are doing and being behind Mercedes and Red Bull is still the target of where we believe we can be.
"I am not getting my hopes up for every race. We try to do what we are doing and continue but we could easily still get a P7 or a P8. I am realistic but hopeful."
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