Usually what would happen would be that the charge would be referred to juvenile court following the arrest of the juvenile or issuance of a citation to the juvenile for that offense by law enforcement. The juvenile court (or the juvenile division of some other court) would then have discretion to impose a variety of sentences if it found that the juvenile was guilty or if there was a plea bargain (plea bargains would typically resolve 85%+ of cases).
The default sentence would typically be a modest fine and/or a brief period of incarceration in a juvenile facility.
But, the juvenile court, often as part of a plea bargain proposed by the juvenile's counsel could call (sometimes with the required approval of the prosecutor) for a "deferred judgment" in which the case would be dismissed as if it had never happened if certain conditions were met, or probation subject to conditions including attendance at therapy, in lieu of a fine and/or period of incarceration. The resolution you describe in your question sounds more like a deferred judgment than a probation sentence, although the differences are subtle.
Instead of therapy, another possibility would be community service, typically as a probation condition.
Therapy or a deferred judgment, in general, wouldn't typically be limited as a matter of law to first offenses, and would be guaranteed as a remedy in any particular case. It would simply be a common resolution in some particular juvenile courts with a particular set of judges, prosecutors and defense attorneys.
In practice, often this kind of resolution (i.e. a deferred judgment conditioned on attending therapy or alcoholics anonymous or both) would be proposed by a private lawyer hired by the juvenile's parents who would offer to pay for the therapy at their own expense.
A public defender for an indigent juvenile would often not have the time to arrange the therapy setup and would not have a client with the means to pay for it, so a fine and/or incarceration sentences and/or community service would be a more likely sentence for an indigent (i.e. poor) juvenile.
Still, a lot depends upon the attitude of the prosecutor and judge. Some prosecutors and judges might be inclined to take a hard line (this is particularly common in minority neighborhoods and in a case where a juvenile had many prior offenses); others might be inclined towards leniency and seeing a prospect for rehabilitation (particularly for a white or Asian defendant from a middle class family without many prior offenses). Similarly, boys would be more likely to receive a more severe sentence, while girls would be more likely to receive some leniency. A younger child would also be more likely to receive leniency than an older one.