Imposter syndrome is common, especially for some cultures, genders, personality types... I'd recommend looking into that to find some help (I'm not qualified for this).
The answer is that you don't need to be hired by Google to be a real developer (only the reverse). The same way you don't need to get invited to the Olympics to do real sports.
I'd also note that there is a fair amount of development word that doesn't need complex algorithms. They're not useless, but you can be productive without it.