Making up a 1/2" difference in subfloor level
I doubt you'll find a soft underlayment that's that thick, 1/2&quot;. You will probably need to lay down 1/2&quot; plywood and then add your flooring on top of that.
There are many reducer transition pieces if you should decide to keep the new floor lower than the existing one. I know you stated you don't want that but it might end up being a viable alternative.