Wars. Can we have new members wait a day or two before opting in to prevent matchmaking manipulation?

Not quite… You are manipulating the matchmaking that way but NOT because of the algorithm getting confused or whatnot…

This is the key here in the process… “NEW” alliance.

With a “NEW” alliance you are manipulating the “Past War history” part of a war score…

If an alliance is brand new, they have no war score…

If we write it mathematically:
[War Score] = [Top 5 Hero Power] + [Top 30 Hero Power] + [Past Performance]
So a new alliance, has the [Past Performance] = 0

So matchmaking for a new alliance is still matching with a similar [War Score] alliance but there [Top 5 Hero Power] & [Top 30 Hero Power] is much larger than their opponent… because the [Past Performance] is zero (0)…

Mathematically, if 1 = new alliance & 2 = older alliance
[War Score 1] ~= [War Score 2]
[Top 5 Hero Power] + [Top 30 Hero Power] + 0 = [Top 5 Hero Power] + [Top 30 Hero Power] + [Past Performance]

Overall

Overall, this process is known as War Hopping or the War Shuffle.

There are a couple threads on this topic, the best ones explaining it are below: