I wish that Trello would include time with the start date, this on the surface seems so simple for them to add and would allow you to do exactly what you are asking for.
I have some tips if you are looking to use Trello for Time Blocking
In the calendar view, the tasks show up in the order they are in their lists so you can sort lists by due date, you will be able to recreate a time-block system in Trello
You can use a custom checkbox field and call it "All Day Event".
When checked, automation can set the start date to that day at 00:00 and due date to 11:59.
You can set up automation rules to make sure nothing else can go into the day
Its not straightforward but it is possible.
I'll add it to my list of Trello community articles to write
