In my experience, the best way to insulate yourself from the pangs of imposter syndrome and unproductive self-doubt is with experience of past successes.
Early in my software engineering career I would constantly and painfully wonder if I was actually capable of fixing a certain bug or solving a new or difficult problem. But then after working hard on a solution, 99% of the time it would work out. After going through this process of debilitating self-doubt and eventual success over the course of years, it has become much more manageable.
I still sometimes panic when initially faced with a very difficult programming problem, but I can put those fears to rest much more easily by saying, "ok, I've solved hard problems before. I may not know how to solve this particular problem yet, but I feel confident that I will be able to figure it out just like I did in the past with difficult problems X, Y and Z."
At the risk of sounding pedantic, part of leaving the beginner phase — and the true value of experience — is developing a kind of armor against those feelings of inadequacy (of course you don't want this to go too far into feelings of overconfidence or an inability to reflect when things do go wrong).
I also think it's the responsibility of more senior engineers to recognize when a more junior teammate might be having those self-doubts and be empathetic while helping them build up their own successes.