Best answer
Do it with a tag. Use the normal DM trigger, check for a tag at the top of the flow, and set that tag on the way out.
There is no separate first time trigger, and a tag is more useful than one would be, because it is a thing you can also filter on later.
The build:
- DM trigger.
- Condition: does the contact carry the tag known-contact.
- If not, send your welcome. Say who you are in one line and what they can ask for. Then add the tag.
- If yes, go to the normal flow.
What to put in a welcome message matters more than the mechanics. The ones that work do two things: they answer the question the person probably has, and they show two or three buttons for the things people actually ask. A welcome that says "thanks for the message, we will get back to you" is a delay with extra steps.
One practical note: the tag persists even if the conversation is later archived, so someone who wrote a year ago will not get the welcome again. That is usually what you want. If you would rather re-welcome people after a long gap, check the contact's last activity date instead of the tag.
The Inbox basics article covers where tags on a contact are visible while you are reading a thread, which makes testing this much faster.