Is there a cassette available with an 11-tooth start so I don’t have to change the 11-speed HG driver on my rear wheel to XDR™?

No, there is not. The 10-tooth start for eTap AXS™ cassettes is an integral component of our X-Range™ gearing design and offers the greatest number of 1-tooth jumps between cogs while still delivering increased overall gear range.