[fwg]

Yes it is.

Big-O means given an arbitrary function of some complexity, it is definitely bounded by this other function from the top, i.e. that other function is always larger than our arbitrary function.

f(n) \in O(n^2) means n^2 (ignoring constant factors) is always larger than f(n). If you have no polynomial elements in your O(g), then you only state the constant factor. Like in O(1).

So saying Cold_start(service) \in O(100 ms) is exactly the same as saying the cold start will always be below 100 ms. It makes sense to not say they are all O(1), although strictly they are, as the interesting bit is the difference in magnitude of the constant.