I have filled some mighty big holes with plastic wood. I don't know if
it will stand up to freezing and thawing though. You'd want to not
just fill it all at once, put some in to block the hole but leave room
on either side of that blob for it to bow out a little before it dries
due to gravity.

You can stain it, I had to use some today and the container said so.
(Always trust containers.)