Hi Julie,
Without seeing pictures of the first aid kit and its contents I can't give you a date. The fact that it's a First Aid Kit No. 20 in a wooden box with an Esmarch Triangular Bandage would lead me to think it could potentially be an older wartime first aid kit, but you mentioned it contains Polysporin, which was not on the market until the 1970s, according to information I've seen. Where did you find the first aid kit? Is it possible that some of the contents are not original and were added later? Would you be able to email me some photographs of the kit through the blog's email? You can find the link to the email on the "About the Author" page of the blog.
Thanks,
Margaret