Yes you can download your Admit Card without having your UPSC hall Card number
Here are the steps you have to follow:-

First you have to go to their site

Than on right side of page click on your Subject criteria

Than you are on a page with options of the subjects, select your
Subject.

Here I am sharing a link from where you can obtain detail of your Admit card.

upscadmitcard.nic.in/IESDefault.aspx