It is not possible to do with the Post Publish Date , however if you create a custom date field where the user enters a date then you can create a frontend filter based on that field.
Do you want to filter by a post type ? can you provide a little more information?
If so then this is not natively possible with our plugin to filter by the post type, however you can use some custom coding to add a custom post type filter.
With the custom field you are able to do a comparison between 2 date fields and filter for posts that are between those two dates. However as mentioned you're not able to do this with the default date field that comes with wordpress. You will need to create a custom field for that date that you want to filter by.
I hope I was able to explain this a little clearer for you.
What you have there is a backend filter. If you want to create a static filter on the backend then you can. This will result in the view always being filtered by this value.
However if you want your users to dynamically filter the view on the frontend then you will need to use a custom field. If you don't want your users to filter from the frontend but have the view filtered by a constant value then you can filter by the Post Date.
Hopefully this clears the difference up a bit more for you.