how long (in general) should it take an unbroken 3 yr old to go from unbroken to trotting exhibition barrels. I know lots of factors come into play but just need a ballpark

Unbroke (never ridden) 3-4 mo munimum, to get him riding decent and get some buttons on him. Just about anyhorse can trot the pattern .  I want him broke enough to llope balanced, small circles before he goes to the pattern, sometimes they need to build strength along with control before they're able to do this.