All the things that gives Initiative in the game:

1. Cave Keys
2. Training Potions
3. Assist links
4. Secret Scrolls
5. Myoboku
6. Battle Armor
7. Having Ninjas
8. Treasure Tools
9. Refines
10. Charms
11. Five Nature Chakra
12. Summon Cultivation
13. Quick rune, in Eigth Inner Gates
14. Purifies
15. Home Bonds

But as of right now, the best way to get Initiative, is through Training Potions.
Spending Moon Coins on Cave Keys, and spending your Sun Coins on Advance Refines, or Epic Refines.
Depending on what you need it the best way to utilize them.