Is hitting the database from most tests normal in TDD? Yes, unfortunately, it's more normal than it ought to be. That doesn't mean it's right, though.
There are various styles of TDD:
- Outside-In TDD, popularized by GOOS.
- Bottom-Up TDD, which is the 'older' style, where you develop 'leaf' components first.
When you use the Outside-In approach, you'd typically start with a few coarse-grained tests to flesh out the behaviour of the system. These might very well hit the a database. That's OK.
However, you can't properly test for basic correctness from the boundary of a complex application alone, because the combinatorial explosion of required test cases is prohibitive. You would literally have to write tens of thousands, or hundreds of thousands of test cases.
Therefore, even with the Outside-In approach, you should write most of the tests at the level of a unit. These tests should not hit the database.
If you're using the Bottom-Up style, you shouldn't hit the database in most cases.
In short, TDD means Test-Driven Development, not necessarily Unit Test-Driven Development, so it may be fine with a few tests hitting a database. However, such tests tend to be slow and fragile, so there should be only a few of them. The concept of the Test Pyramid nicely explains this.
If you want to learn more, you may want to watch my Pluralsight courses