How to upload an image with static URL on Firebase Firestore

Okay. So I'm building a system where users have to upload their profile picture.

After uploading and getting the URL, I store it in various collections in my database. The issue is, when a user updates their profile pic, I'd have to update all instances of the profile pic on my database which is quite cumbersome.

I want to know if I can update a profile picture with the same URL as the previous one, so that all URLs on the database would be unchanged but dynamic...