Imagine if they assign you a public defender because you can’t afford counsel, but he/she arrives ten minutes before your hearing and has no

I'd cop a plea.

Let's assume this results in your conviction.

IF you could later obtain the help of competent counsel, this lack of preparation by your trial attorney could be grounds for a mistrial.  A judge might not grant it (these things are always somewhat uncertain), but it is a legitimate complaint.

I have that had happen and it has always worked in my favor.  No questions asked.  The answer. I was not guilty.  And I wasn't.
:) :)

More facts needed.  Which hearing?  Judges do know how busy public defenders are and almost expect them to ask for a continuance because they are not ready to begin the litigation process in the present case.  This is not ineffective counsel, it's reality.  They will get their continuance and if they do not, it will be helpful on appeal (if it goes that way).