How do I put a word-press blog into my static site without installing wordpress on server?

I think that you should have a look at the WordPress API.
https://developer.wordpress.org/rest-api/reference/posts/#example-request

It allows you to fetch all posts with Javascript or any other language.

e.g.

jQuery.ajax({
    type: 'GET',
    url: "http://example.com/wp-json/wp/v2/posts",
    success: function(data) {
        var obj = JSON.stringify(data);
        var result = jQuery.parseJSON(obj);
        console.log(result);
    }
});