Anecdotally: The best jobs I've had were ones where I was able to contribute to the team on day 1 or 2. The worst jobs were the ones where it took me 3+ weeks before I got assigned enough permissions to make a single change.

Which goes a little against the idea of slowly introducing trust, but these were sysadmin/devops jobs, not coding. YMMV.

EDIT: By "best" I mean "most productive, most enjoyable, most memorable". All accusations of selective memory or bias on my part are of course accepted.