It's almost completely GM territory. The words "acquired" and "inherited" reference how a creature might come across a template; but they're very broad categories.
Inherited Templates are just the way the creature is, that they were born that way and (barring magical hijinks) will die that way.
Acquired Templates are something that happens to an entity, it's transformative - the creature had certain properties before the template and different properties afterwards. Some like, Lich have rules that cover prerequisites (creating the phylactery), but there are no actual rules for the final transition. Others, like Mummified provide more detail. The GM will have to fill in the blanks to fit the story.
Depending on the nature of the template, there's no reason that a creature could not be "born" with an Acquired Template - after all, Young is an acquired template that eventually goes away.
In your specific example, a character might acquire an Advanced animal by going to a breeder and selecting from the prime stock. It would probably come with a premium, but getting the "pick of the litter" always does. If you wanted to extend it even further, you can double up on templates. A Young Advanced Dog, perhaps - he's not magnificent yet, but a skilled breeder could see the potential.