Hi Katya. It looks quite a bit like Pittosporum tenuifolium 'Silver Sheen' to me. Silver Sheen is a fast growing shrub/tree that tends to pop up everywhere as it grows wild and is often used in ornamental gardening. Wonder if that could be it.
Ha! Indeed, we are in the West Koots, and yes, I think you are probably exactly right... Black Cottonwood is my guess too.
I am thinking of trying transplanting one our in front of our yurt. They seem to grow really fast and I need a good fast growing tree, as we are in an off-grid yurt, and it gets horribly hot inside w/ no A/C.