If Hashirama was still alive at the death of Tobirama, Tobirama would hadn't bother with picking up Sarutobi as successor.
Also, we don't actually know WHEN Sarutobi became Hokage: while IIRC the earliest Sarutobi with Kage clothes is shown being quite older than the Sarutobi at Tobirama's death, that doesn't imply he wasn't Hokage in the meanwhile.
Also, we don't actually know WHEN Sarutobi became Hokage: while IIRC the earliest Sarutobi with Kage clothes is shown being quite older than the Sarutobi at Tobirama's death, that doesn't imply he wasn't Hokage in the meanwhile.