For several reasons it makes sense to go early in the day if possible when purchasing challenges.
There is a counter thought to the idea of reserving play on daily games until after you purchase. If you are seeking the green epic challenge specifically and to a lesser degree..the yellow, it may be helpful to onow your scors on daily games first, especially any you chronically struggle with. I have missed on green twice now due to a low score earlier in the day on one of the associated games. Subsequently, I now also play World Quiz, New Question and Daily Game early as part of the" pre flight check" routine before buying a challenge and will scrub a planned challenge purchase if the aggregate total of those three plays doesnt hit a certain minimum total.
While this is at odds with the sound "wait and see" strategy already mentioned in this thread, and drawing epics at all is rare, much less getting either the green or yellow flag specifically, over the long haul, an instant red X on a purchased daily that comes out as easy/medium/hard is nothing next to an instantly missed Epic and so that wins out as the primary driver of ourchasing strategy for me.
It all depends on what you are after at the point in time when you are making the purchase