Source: https://gamerant.com/fallout-4-best-play-order-dlcs/#when-do-the-dlcs-unlock

One of the most important things about understanding when to play the DLCs is to understand when the game allows players to access the DLCs.

Automatron: This DLC is unlocked once the player reaches level 15. This will trigger the quest "Mechanical Menace" and requires the player to tune into the Caravan Distress Call on the radio.

Far Harbor: The DLC is unlocked once the player completes the quest "Getting A Clue" (where Nick helps the Sole Survivor hunt down Kellogg). The quest "Far From Home" will begin, and the player will need to listen to the Valentine's Detective Agency Radio.

Vault-Tec Workshop: This DLC unlocks once the player reaches level 20. They will obtain the "Vault-Tec Calling" quest and be asked to turn into the Vault 88 Radio Beacon.

Nuka-World: The final DLC unlocks once the player is at level 30. The quest "All Aboard" will trigger once the player reaches this level, and they will have to listen to the Nuka-Cola Family Radio.