SQL DBMS come with an obvious text-only schema management tool called SQL-in-text-files. If you don't need anything esoteric, number them in order of application (001-base.sql, 002-add-customer-model.sql, 003-trigger-on-name-update.sql...), and you are good to go. Any VCS can deal with those properly.
I've used plenty of saner version control systems than Git, and I wouldn't want a database to restrict me to it (even though I am usually "forced" to use Git nowadays).
I would just suggest people use database migration tools from the start. This "autoincrement" method breaks down easily when there are multiple developers working on the same project.
I was on a team doing this 15 years ago, and we did some pretty hardcore DB migrations on a large, complex database without any fuss with >30 developers working on it at the same time.
There are hundreds of “schema upgraders”, all based on their flavor of XML, JSON, text files and their associated name comventions, precisely because the canonical SQL way of doing it is limping.