Unless you are extremely well trained, it is not possible to travel between Russia and Alaska without taking regular, scheduled flights. You will not be able to board those flights without a US visa.
As an alternative, I would recommend cycling from Russia to Norway. Many refugees from Syria and Afghanistan have discovered this route. Take the train to Murmansk, then
train¹ bus to Nikel, then ride a bicycle to the Storskog border crossing where you can seek refugee status (travelling on foot is not allowed and hitch-hiking will get the driver into trouble, but taxis reportedly can bring you to 100 metre from the border). Note that it will soon be winter and temperatures well below -20°C are quite possible, so you might want to wait until spring (that means June).
¹Apparently, passenger trains to Nikel have been cut.