There are an increasing number of very well known airlines today who put 200 hour ab initio pilots straight into 747/A340/777 long haul operations.
If you consider the usual SOPs regarding the use of autopilot and that many would be very lucky to get 20 sectors per year (post cruise pilot years) I would guess that the average amount of hands on per year would be in the order of 100 minutes. Of course, the hands on would mainly come after the aircraft has been configured and stabilized 4-6 miles out by the autopilot.
So some 10-15 years down the road when command comes around they would have, post initial training, about 16 to 25 hours of handling, in 2-3 minute bursts, under their belt.
To quote the old joke, I think I've got more time in the flare
Just a thought