Can reaction spells be cast without any trigger?

I’ve come across a few questions regarding the spell storing ring to which my question matters. Under spell storing ring it reads:

Any creature can Cast a Spell of 1st through 5th Level into the ring by touching the ring as the spell is cast. The spell has no Effect, other than to be stored in the ring.

So to store a spell in the ring you cast the spell. Shield or absorb elements have a casting time of a reaction, can they be cast without a trigger? In particular, in our game the need came up to store reaction spells mid-combat. But the casting time of these spells is a reaction, so the question came up can you use your reaction without a trigger?

Under rules for spellcasting there are 3 blocks that give some guidance on casting time:

Each spell description begins with a block of information, including the spell’s name, level, school of magic, casting time, range, components, and duration. The rest of a spell entry describes the spell’s effect.

Most spells require a single action to cast, but some spells require a bonus action, a reaction, or much more time to cast.

Some spells can be cast as reactions. These spells take a fraction of a second to bring about and are cast in response to some event. If a spell can be cast as a reaction, the spell description tells you exactly when you can do so.

Rules for combat has this:

Certain Special Abilities, Spells, and situations allow you to take a Special action called a Reaction. A Reaction is an instant response to a trigger of some kind, which can occur on Your Turn or on someone else’s.

Combining these, we know that the spell block contains the casting time, these spells have a casting time of "1 reaction". We know these spells take a fraction of a second to bring about so they are fast, it seems requiring an action or bonus action for it to be cast is unwarranted. However, it also says if a spell can be cast as a reaction, the spell description tells you exactly when you can do so. Furthermore "a reaction is an instant response to a trigger of some kind."

Does this mean you can’t cast a reaction spell without the trigger? Does this imply that you have to get hit to store the shield spell into the ring?

Can a mage cast shield or absorb elements without getting hit or receiving elemental damage? If so, when can they take their reaction to store the spell in the ring, I’d presume it would have to be their own turn (using their reaction just to store the spell), but can they react to nothing off turn to store the spell?