It is not about trust. It is that a date somebody has paid something towards is a date they turn up for, and a date they have not is a date they will move when something else comes up.
It also means the materials for the job are not being financed out of your own pocket while you wait to be paid for work you have already done.
Say it plainly when you quote — a deposit secures the date, the balance is due on completion — and put it in writing. Almost nobody argues. The ones who do have told you something useful.