I was claiming it is impossible (from this angle), and now I still do.
Reasoning:
You have a 7 card hand, and draw on turns 2 and 3 (can't play card from turn 4). You have 9 cards to work with.
To use both the entropy and aether nymph, You must make them both by turn 2.
Your queen must make the other two nymphs, and hence must come a turn earlier, namely turn 1.
Turn 1: Nymph queen, Sor it
Turn 2: Turn pillar into entropy nymph, some chrysoras
Turn 3: Antimatter your nymph, Turn pillar into aether nymph, remaining chrysoras.
Turn 4: Quint nymph.
Turn 5: conditions met.
This is one turn AFTER your requirements. I don't care about quanta.
Hence you must have 2 nymph tears, or a tears and a queen.
2 tears is impossible, as that takes 10 cards (4 chrysora, 3 pillar, sor, 2 tears)
So you must use queen, tears, and ONLY 2 towers.
With 2 towers, you can't play your queen turn 1. Hence you must play it turn 2 earliest. Hence one of the three nymphs comes out on turn 3, earliest. It can use it's abilites on turn 4, one turn too late.
No solution, Q.E.D.
Of course, i could be missing someting obvious