Existing databases
Two ways into the history: adopting a database that already matches, and accepting a change you migrated by hand.
A database without history
A database that hbm2ddl created has no history and is refused by default. With adoptExistingSchema the executor records it as revision 1 without executing DDL, but only if every table and sequence of the target exists and the database matches exactly.
The one common difference
Hibernate names enum CHECK constraints the PostgreSQL way, the framework after a hash of the column ID. The refusal lists both names; rename the constraint and start again.
The executor also compares each check's definition, so a renamed constraint passes only if it enforces exactly the modelled values. An @OrderColumn's position >= 0 differs from the modelled range and must be replaced.
Changes the executor cannot plan
Type and primary key changes, among others, need a data migration and are refused. The refusal names the target's fingerprint. Migrate the database by hand to exactly the target, then start once with that fingerprint.