As far as I know, the answer to your question of "how do most opioid addictions start" is not known. I am not aware of any studies or surveys that have credibly and thoroughly addressed it.
If studies like this are going to be done (and I'm hopeful they will), they'll need to start at the beginning of the chain of custody (for lack of a better term) and end at the end of it.
Pharmaceutical company
Company manufacturing for pharmaceutical company (they are sometimes different)*
Large scale distributor *
Smaller scale distributor*
Medical networks (Blue Cross, Medstar, etc)*
Individual medical offices*
Individual doctors*
Individual patients*
Those marked * above are ones with the potential for redirecting drugs to places they don't belong.
Then on the illegal side there are
Large-scale criminal drug networks
Smaller scale dealers
Individual dealers
Individual users
Those stealing directly from a family member, friend, person for whom they're a caregiver, etc.
Robbers (people actually do wait for someone to obtain drugs, then rob them)
That's a lot of potential hands handling opioids, and rather than pick 1 or several groups to study we're going to need to know how much each group contributes to misuse of opiods in the US. Because opioid misuse affects millions of people badly, not just the users. There's a lot of hell being paid by people who don't deserve it (families mostly).