I don't think there are any tools to auto-generate deltas, though you can generate an initial state. Once you get accustomed to the new work pattern of writing the changes then just applying them it becomes a smooth experience. It also gives better control over the changes done and nothing unintentional is added.

I implemented it with my previous employer and even though a significant portion of the ~40 developers were used to making changes straight in the database then writing manual SQL scripts for making those changes it went great with the adoption. In our case we had tons (~5000) stored procedures, functions and views that had to be version managed, so I extended the capabilities of Fluent Migrator to specifically deal with that better. Extending the functionality is rather easy, even without forking. Unfortunately I can't share the code as I didn't have time to convince management to FOSS it before I left that place.