In fact, one of my main worries is that it's difficult to leverage Progress' opener if I don't open very early. Compare with Authority: you don't need Authority's opener before you have a couple warriors/archers to hunt barbs. And, when your squad is up and ready, you will have opened Authority anyway, even if you delayed your monument for a shrine (and maybe a warrior).
By contrast, you want to open Progress ASAP to get yields from the opener; if you wait a little too long, you may open just when your capital reaches the size (usually 4) where growth slows down noticeably in an infrastructure-lacking capital city. You will get some science for already existing population, but you would have preferred getting the instant yields on growth both for science and culture.
Actually, can it be optimal to slow growth down by focusing on production before opening Progress, for example when the capital hits size 2? This way, you may get both your monument and your shrine up earlier, as well as more yields from Progress' opener. The trade-off being that postponed citizens may have been put to good use.