Tyre bulge when inflated, new

Got some new bicycle tyres yesterday (CONTINENTAL COMFORT CONTACT 700 x 32c CITY COMMUTER ROAD) The tyre I fitted to rear wheel seems to have a bulge in sidewall. Took it off, looks ok inside. It feels perhaps a bit thinner where its bulging. The tube seems a bit big for the tyre but I doubt this could cause it?!? and the front is ok with same tube. Previous tyres were 35c.

The bulge is perhaps 10mm diameter and 1-2mm deep. Not very visible but immediately feel it if rotating the wheel.

They were from an ebay shop and arrived twisted / folded in half so as to be much smaller to post – wire bead type. They seem to spring back into normal shape when unpacking them, no visible damage. I assume the folding may have stretched/torn a cord?

Edit, I did remove, inspect, rotate and refit the tyre. The bulge was in the same part of the tyre, so its not the tube. I inflated to about 65psi. Recommended on the label is 70, max 85.

I did see the other post, but that is showing a used, damaged tyre, rather than a brand new one. Thanks I will be sending it back.