I opened an Advance Trailblazer Chest and got a piece of rubber, but where did it go?

Parts materials like rubber and sensors are found in the Parts Factory Building. This is where they are made (if not bought) and then combined and crafted into parts.

Tap on the parts factory and choose the Depot option. Then select the materials tab at the top and select the trailblazer option if its not already selected. Here you will see all the materials you have collected for that part set.