Flutter web with Firebase Hosting can not load pictures from storage

I'm developing a flutter web application and when I run it on the debug mode (local host) it works as a charm, my firestore requests works and storage urls too, but when I deploy it to Firebase Hosting, I can't load the pictures using the url from storage. This is what I get:

Access to fetch at 'https://firebasestorage.googleapis.com/v0/b/url-to-my-picture/?token=firestorage-key' from origin 'https://my-project.web.app' has been blocked by CORS policy: No 'Access-Control-Allow-Origin' header is present on the requested resource. If an opaque response serves your needs, set the request's mode to 'no-cors' to fetch the resource with CORS disabled.

I searched for this and I got that I needed to set up my hosting on the firebase.json file and this is what I've done on the hosting section:

  "hosting": {
    "public": "build/web",
    "ignore": [
      "firebase.json",
      "**/.*",
      "**/node_modules/**"
    ],
    "rewrites": [
      {
        "source": "**",
        "destination": "/index.html"
      }
    ],
    "headers": [
      {
        "source": "**",
        "headers": [
          {
            "key": "Access-Control-Allow-Origin",
            "value": "*"
          }
        ]
      }
    ]
  },

But no success. Note that I'm only using Flutter Web and the Firebase itself. No NodeJs, no php.

EDIT: This is how I load the picture:

...
NetworkImage(
    pic.url,
),
...