Can you guarantee a DM will reach the Primary inbox?
No. Instagram determines message routing and inbox placement, and users have their own message settings and relationships with accounts. There is no reliable method that guarantees a cold outreach message will always appear in the recipient's Primary inbox.
The practical approach is to send relevant, genuine and respectful messages, build legitimate interactions, follow Instagram's rules, and avoid behavior intended to bypass platform systems. That's what the rest of this guide covers.