Perhaps contact your HR department and find out if they're doing anything for the family. Also find out if they know anything about the funeral arrangements so you could potentially do something directly. If you're not nearby sending flowers and that kind of thing is a thoughtful gesture.
It was quite a few months after starting when colleagues quietly offered their condolences, since the news was already circulated to various teams explaining my initial absence when I was due to start.
Their restraint to offer thoughts immediately on day one (after being introduced) was greatly appreciated.