The one time I tried raising bilimbi I planted a flat and I think they almost all came up in a week or so. They were fresh from the fruit, so that might have something to do with it. I noticed that carambola seeds also would sprout quickly if taken directly from the fruit, but if somewhat dried (even for a couple of days) they would become semi-dormant, and straggle up in the seed flat over a month or more.
Hope that helps.