On a cow-calf operation, which is where most beef production starts, a typical cow will graze and/or eat hay for about 12 years while breeding, then get slaughtered pretty much the day they're shipped because they aren't worth fattening at that age, they're just going to ground beef.

The culls (mid-life cows, failed to get pregnant) might see a couple months of their at least 36 month existence on grain before slaughter. Older ones might just go straight to slaughter.

Steers and cull heifers (which is most of what gets used for choice cuts like steak) typically see about 14 months typically on pasture and silage/grain being backgrounded on farm, then about 3 months being intensively fed in a feedlot at up to 80% ration before slaughter.

So, by far, the largest proportion of feeding of most cattle is by grazing or stored forage as part of the backgrounding process. It's only when they enter the feedlot that it becomes a grain-intense operation, and that part of the production is very short because feedlots don't make money feeding cows from calf-age to slaughter.

Also, many larger cow-calfs will also hold on to steers and push them, selling them as "fats", which sees much less intense feedlot experience. This isn't a huge proportion of the final months of most steers, but is still an appreciable proportion of the market.

The stockyards of Kansas aren't the typical beef production scenario. They're just very visible.

basically all beef cattle graze for the first year or so.