Find your tribe in a Sea of Creativity
So, there's a relatively common headcanon where Hawks can and does enjoy making nests like any normal avian would.
However, I like to imagine that since Hawks was raised in the HPSC, where they would only hone certain skills that are actually useful as a hero, his nest making skill were never improved or taught.. Ever.
His father certainly never taught him, and the HPSC would have deemed such a skill useless in the grand scheme of things.
So, Hawks would have never learned how to build a nest. However, he does still have instincts for it.
Hawks would, in my mind, probably make a nest exactly like how pigeons do.
Pigeons are well know for being absolutely awful with nest making, using scraps of whatever and laying them out in whatever fashion they feel is fit so high up in the safety of tall buildings or mountains.
Hawks, having very little valuables already, would probably have a scrappy little pigeon nest, because it's all he knows how to make. It's all he can do, because he was never taught or has been unable to build upon the skills needed in nest making.
The Endeavour doll would absolutely be in the nest too by the way.