Of course it's logically possible and the reason is contingency would be nonsense without necessity.
This is just pathetic. You're basically saying that you can't imagine why stuff exists and is as it is, so you're just going to make up something really, really magical, that magically doesn't need a reason to exist, but somehow does have a reason to exist as well, by magical, magic, magically. There is no hint of logic or reasoning involved.
Unless you can give an actual sufficient reason as the why a 'necessary entity' couldn't not exist, then you're just playing silly games with words. What you've got is no different to a brute fact.
Weirdly enough Krauss and co are trying to establish that there cannot be nothing. They have missed that there is already a solution to this established by the principle of sufficient reason which Carroll is seeking to disprove.
But your magical magic, magically necessary entity doesn't follow the PSR because you can't give a sufficient reason for its existence, at least in any why that distinguishes it from a brute fact or isn't entirely circular, i.e. by seeing that things exist, and thinking there must be something with sufficient reason to explain it, because you can't imagine/won't accept anything else. And even if we followed that circularity, it would tell us exactly nothing about what said 'entity' would be like.
If we ask why something and not nothing the explanation for that is the necessary entity...
Except it doesn't answer that question.
...and since it could not have been derived from nothing then it must necessarily have always existed...
Back to Newtonian thinking about time. The universe has 'always' existed because time is part of the universe, so it has existed at every point in time.
...or alternatively after the explanation for why something rather than nothing...
Still waiting for anything remotely like that explanation. You're just going round in circles.
Now it seems to me that Russell's use of Brute fact has no explanation at all...
Exactly like your 'necessary entity'. The only difference is that you're trying to assert that it does have sufficient reason without actually being able to say what it is.
...and is a consequence of no logical pathway at all.