Once you've announced that you're casting a spell, players can't take actions until you've finished doing so. Notably, opponents can't try to remove cards from your graveyard to stop you from collecting evidence.

Cryptex's first ability is a mana ability. It doesn't use the stack and can't be responded to.

If you can't exile enough cards to meet or exceed the required mana value, you can't choose to collect evidence at all.