The disadvantage of spring seeding is that the root system won't be developed enough to endure hot weather. It is nice though, this time of the year, to not have to worry about ever colder weather which can lower the blinds on seedling growth (like last fall here).
I'd spread an inch or less of topsoil on it, feather it into the surrounding grass, seed it and rake it in (and water it as needed). You might need to hit it again in September, but I'd take my chances - you don't want to be looking at that all summer, lol.
Eta - if you don't have one, get one of those 3 ft. wide aluminum dirt rakes, they're great for that kind of thing.