If I'm correct he waited for her to say it, Oscar thought he's very selfish that he kept reincarnate her over and over again and doesn't want to force her on anything again but at the same time she is always busy with her duty from position she got in every reincarnation to the point she never relieze her feeling or Oscar's feeling. (〜￣△￣)〜
I don't think he'll be forcing her if he courted her. I mean, it doesn't mean he'll tell her that they're lovey dovey in their past life. He will be courting the current her and the current him. And what's with the "waiting for her to realize her feelings?" Didn't she forgot about their relationship? That means she basically forgot her feelings to him as well. Correct me if I'm wrong, but isn't our brain the one that directs our feelings? So in the normal sense, if we forget something, so goes our attachment with it, right?
That's also why he wait for her to remember him herself
But if he doesn't make an effort for her to remember, then the chances of her remembering or an event happening that will trigger her memories is almost nil; as proven by how many times she's reincarnated. Besides, it doesn't really matter if she remembers or not right? The only important thing is that she'll love him. Because "they're for each other."
Well, only the author know the answer ╮(￣▽￣)╭
Why didn't Oscar and his previous selves just courted her? Isn't his wish for her to be happy in her next life? And since he's the only partner for her, what's stopping him from courting her so that she'll be happy? I don't recall anything that forbids them to be a couple if she doesn't regain her memories with him.