Yes, it's possible. But...
BE AWARE that cloning doesn't always work. Seems to work for some, and not for others.
I realize this statement sounds nebulous, but it is what it is.
ANOTHER WAY you could accomplish what (I think) you want:
- have your external SSD formatted (APFS) and connected.
- boot to startup options, choose options
- this should give you access to the OS installer
- since you're still on Sonoma, I will GUESS that the version of the OS it offers at this point is Sonoma. If it offers you Sequoia or Tahoe instead, there are "other ways" to get to where we need to be (not discussed yet)
- open the installer, but be careful when it asks you to WHERE you want to install.
- "aim it" at the external SSD and let it go to work
- do you get a "good install" on to the SSD?
OK, then, begin setup on the SSD, but again, be careful.
You don't want to create a "completely new" account on it.
Instead, use setup assistant to migrate the contents of your internal drive to the external.
When done, you'll have "all your stuff" on an external SSD running Sonoma.
It's not really "a clone".
But the results should be nearly identical.
As I said above, the SuperDuper cloning process may work.
That's the easy way.
But if it doesn't work for you, my "alternate method" SHOULD work.
Sometimes one just has to do, what one has to do...