Alison - Give it time. I hear from your post a sense of feeling pressured. You do not need to be on your H's timeline.
He just started IC and might be feeling that initial thrill of making a lot of progress. I know from my own experience that IC has its ups and downs, and it is hard to stay consistent over the long-term. It's easy to say "I need to show you through actions". Great... those are still just words. Perhaps it will stick, perhaps it will not. If he really wants it to work, he will be patient and continue to make an effort. He will be okay with you needing time and space to sort things out.
You also mentioned that you haven't given him opportunities to show you progress through his actions, but then you spelled out exactly what he can do: Demonstrate first that he is a good father.
