Nice to know there is new hat collector out there!
I would place that in the early half of the 1950s. It was made by using a basic hat block. The foundation is buckram, rather a thick buckram at that. The buckram was blocked by steaming or wetting it and then placing it over the hat block to shape it. After it dried it was removed, trimmed to shape, and the trims glued or sewn onto the buckram base. It looks like the thin ivory colored cord is a satin covered gimp (an old fashioned term for satin cording). The fatter trim looks like a stuffed rayon cording or tube trimming. The top "lace" looks like a pre-made applique. The edges are trimmed in velvet piping and the brim is probably wired under the velvet piping (I cannot tell from the photo).
It is sort of Calot shape. I personally do not think it was worn by a bridesmaid as the color is not common for that, and the style is really a fairly basic cocktail, church style, late afternoon luncheon hat of the early 1950s.
It is pretty, but I do think it was not made by a professional milliner, or was made by a milliner who was still practicing her craft. The heavy buckram is not the usual choice (a finer grade or a patterned French net is more common) and there should be little (if any) of that buckram showing through to the top side of the hat. Buckram is not meant to be seen. The trims should be sewn on, not glued, but you do find glued trims on many home made hats or lower priced hats of that time.
If you want to replace the veiling, may I suggest that you try to find vintage veiling if at all possible. The new stuff is just not the same quality or look.
Thanks for sharing your find with us.