There are a variety of tips and tricks for abilities, trinkets and more that can be used right before you start the key.  Generally, it is spells with a CD >5 mins, but will also need to be something long enough to still be active after the key timer to actually begin the run.

To do it properly, you need to do it right before the key is STARTED, not when the timer to actually start the run begins.  So do a pull timer for when you will hit the start button in the UI for entering the key.

Warlocks

Warlocks can Soulstone twice by soulstoning someone (usually a healer for wipe recovery) before the key starts.

Demon Hunters

Demon Hunters can Meta

Frost Mage

Icy Veins (keeps the 10% artifact weapon damage buff).

Hunters

Hunters can Trueshot.

Death Knight

Death Knight’s Army of the Dead.

Druids

Druid Incarnation (Bear, Boomkin, Resto only).

Shamans

Resto Shamans can no longer hero to get the “healer hero” proc from their legendary weapon.

Trinkets

Healers using Deceiver’s Grand Design can put two bubbles on players before the key starts, and then can put two more bubbles on players after the key starts.  This can make this trinket pretty strong for the first couple of minutes of a dungeon, even if you swap out afterwards for a better one.