Glad you had lift off! How long did it actually take since pitching?
I've had some nerve racking times in the past (before using liquid yeasts with appropriately sized starters) where it took 3 days to get any visible signs after pitching dry yeasts. They were always rehydrated before pitching.
Liquid yeast and starters:
According to White Labs most yeast starters made from liquid yeast should be completed within 24-48 hours:
"When using a stir plate, 24-48 hours is generally enough time for a starter to be completed."
https://www.whitelabs.com/news-update-detail?id=52
I'd take that statement with a large grain of salt. Surely, fresh yeast at White Labs themselves may behave that way.* I seriously doubt that model fits a normal distribution a typical homebrewer will experience.
Especially when the (liquid) yeast is not all that fresh or was stressed during shipment/storage etc. as many of us experience when buying (liquid) yeast from our LHBS or mail order.
* When making new starters using my own
fresh yeast, in good health, such as from a recently crashed previous starter, I have foam within mere hours (3-6 hrs). So I too expect those starters to be completed in 24-48 hours, yes.
That would be the best course of action, when a pitch seems to fail, awaiting a new supply.
However, making a pitchable starter from liquid yeast in that short time frame can be a dime on its side too, depending on how fresh/viable that yeast is. Most will therefore recommend repitching with a dry yeast, even if it's not quite the one you intended. You'll still make good drinkable beer.
You may even want to drop to 28-30F, or even a tad lower, so it starts to get slushy. That will slow down wild microbes from taking over significantly. Just don't do it in glass vessels! Kegs would be fine or plastic buckets.