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You need all of that (structures, algorithms, confidence, etc), especially if you're going for a FAANG. But the biggest thing I see new grads lacking is the ability to communicate and collaborate effectively in the workplace and on teams. At most smaller startups that's maybe even more important than raw ability.

Find any way you can to gain practical experience. Internships, consulting, open-source. Really anything. The bonus is that you'll gain confidence through this path as well. You'll know you're capable of doing the full job (not just the work).