Mithril Coat

• WOTC Official Reminder Textofficial rules
  Indestructible — Effects that say "destroy" don't destroy this permanent. A creature with indestructible can't be destroyed by damage.
• WOTC Official Reminder Textofficial rules
  Equip — Equip [cost] ([cost]: Attach to target creature you control. Equip only as a sorcery.)
• WOTC Official Reminder Textofficial rules
  Flash — You may cast this spell any time you could cast an instant.

• WWizards of the Coast2023-06-16
  Official Ruling
  Mithril Coat doesn't enter the battlefield attached to a creature. Instead, the Equipment enters the battlefield and then a triggered ability attaches it to a creature. You may cast Mithril Coat even if you don't control any creatures.
• WWizards of the Coast2023-06-16
  Official Ruling
  Attaching an Equipment with its enters-the-battlefield triggered ability isn't the same as using its equip ability. You don't pay mana for the attachment, and the timing restrictions for equip abilities don't apply.
• WWizards of the Coast2023-06-16
  Official Ruling
  If the target creature becomes an illegal target, the Equipment remains on the battlefield unattached.

Rulings via Scryfall