After failing 3rd time you will not get slot soon?

The first 2 tests, you get accses to some more times not everyone sees. Everyone thus gets a chance to do it.

If you want a test really soon, look for canceled tests. Somtimes someone will cancel last minute and you can then easly pick up a time on short notice.

For example: On one testing center i checked you would have to wait until June 4th to get a driving test - but checking a few times in a day I could find one on May 20th and even April 29th. You just have to look constantly and book if something comes up.