from pydantic import BaseModel, Field
import time
import json

class SeededModel(BaseModel):
    seed: int = Field(default_factory=lambda: int(time.time() * 1000))
    sensible_default: bool = False

class Base(BaseModel):
    settings: SeededModel = SeededModel.construct(sensible_default=False)

config_schema = Base.model_json_schema()
print(json.dumps(config_schema, indent=2))

output:

"settings": {
  "$ref": "#/$defs/SeededModel",
  "default": {
    "sensible_default": false
  }
}