I attach figures of ice drift predicted for today, Jun 1 & 2 (HYCOM+CICE model). Also the model predicts what can be the opening of a large ice front along the Siberian Coast in one week (bottom image, sorry for the sizes!). Add up the already open front on Beaufort, Chukchi, and Kara.
The speed of this front during June should increase with preconditioning (high in Beaufort and Chukchi, nonexistent yet in ESS and Laptev), compaction, transport (will happen during the first week), insolation of open water, and weather (getting better in Eurasia, worse in America, then who knows).