Yes, it is possible to some extent. You can turn off your read receipts in your Instagram settings. This way, when you view someone's story, they won't be notified that you've seen it, which can be a form of secretly watching.
Another option could be to view the story when you think the person who posted it is less likely to check who has seen it. For example, if it's been up for a while and they've had a lot of views already. But this isn't a foolproof method of secretly watching. Turning off read receipts is still the most reliable way within the Instagram app itself.
Well, technically you can try to use third - party apps that claim to allow you to view IG stories anonymously. However, be very cautious as using such apps often violates Instagram's terms of service and can get your account in trouble. It's much safer to just turn off read receipts if you don't want others to know you've viewed their stories.