If you edit a non-raw (e.g. a JPEG) or a DNG (whose camera isn't supported by LR), you won't see Adobe Color. To quickly verify what type of file you're editing, in Develop type "i" to see the filename in the overlay in the upper-left corner.
@johnrellis would be correct here - unfortunately you will only see the multiple color profiles with a raw image file (ex: .ARW files with Sony Alpha Cameras).
Since a jpeg contains processed/less data than a raw file, there is no way to convert a jpeg to a raw file - and as far as I know, there are no workarounds here. In the past I've tried saving as Photoshop Raw, online converters, etc.
With some small tweaks in the basic panel you should be able to achieve your desired look! 🙂