There's no particularly good way to distinguish between available items that have passed their start date and available items which have no start date, unless that is the only characteristic that concerns you.
Now, if you can make some assumptions about which items will have start dates and which will not, you may be able to make some progress. For example, maybe the items missing start dates are all personal tasks, and you don't want them showing up when you are selecting work-related tasks. If you organize your projects so that the personal tasks are in one folder, and the work tasks are in another, you can use the Focus command on one folder, then enjoy a view showing only tasks from that folder. When you construct a perspective, there's a set of checkboxes in the Perspectives window that controls whether or not the perspective restores the selection and focus in place at the time the perspective was created.
Another approach might be to use RobTrew's
Where in OF script. You can't use it to construct a dynamically updated view like a perspective, but you can use it to get a more fine-grained search, and invoke it as needed. Run the search, pick a task, do it, repeat. Or run the search, flag a bunch of tasks, do them, repeat. The search script gives you a list of matching items, from which you can select any subset to be viewed in an OmniFocus window. Sometimes that window will include other items (the script cannot construct any windows you couldn't construct by hand) but your matching items will be selected. You can save favorite searches for easy reuse, and you can do boolean combinatorial logic, so if you wanted to frequently search for available tasks with both a start date and a due date assigned, for example, you could do so.