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As a Loxodon Druid I plan on "hulking out" into an Elephant using Wild Shape.

The question came up: If I'm in a small corridor and I Wild Shape into an Elephant, can I choose the size of the Elephant to be small enough to fit in the corridor? Is there anything in the rules saying you assume a certain size based on the beast? Not necessary going from huge to tiny, but do I get to choose where on the "huge" scale I end up?

Kind of, with a little wiggle room

I'm assuming your druid is Circle of the Moon since without Circle of the Moon, you are limited to CR 1 wild shapes maximum, per the Beast Shapes table:

2nd | CR 1/4 max | No swim or fly speed | Wolf

4th | CR 1/2 max | No fly speed | Crocodile

8th | CR 1 max | Fly or Swim speed ok | Giant Eagle

Circle Forms for Circle of the Moon says:

The rites of your circle grant you the ability to transform into more
dangerous animal forms. Starting at 2nd level, you can use your Wild
Shape to transform into a beast with a challenge rating as high as 1.

Starting at 6th level, you can transform into a beast with a challenge
rating as high as your druid level divided by three, rounded down.

A circle of the moon druid can transform into a beast with a CR of 4 (elephant) at level 12 and above.

Wild Shape says you use the stat block of the creature you transform into:

Your game statistics are replaced by the statistics of the beast, but
you retain your alignment, personality, and intelligence, Wisdom, and
Charisma scores.

An elephant is a Huge Beast according to its stat block. So if you turn into an elephant it is always a Huge one. The wiggle room is that you could probably make the elephant vary in size within the range of Huge for flavor, with DM approval, but it will always be huge. This means that you are subject to the restrictions of a Huge creature.

No, the druid assumes the beast's size and other physical statistics.

When a druid uses Wild Shape, most of their stats are replaced by those of the beast.

While you are transformed, the following rules apply:

• Your game Statistics are replaced by the Statistics of the beast...

The beast's size is part of their statistics. So if you Wild Shape into the form of a huge-sized elephant, then you become huge-sized.

However, note you can squeeze in spaces that are one size smaller.

A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that’s only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on Attack rolls and Dexterity Saving Throws. Attack rolls against the creature have advantage while it’s in the smaller space.

For example, a druid Wild Shaped as a huge-sized (15 ft wide) elephant could squeeze through a large-sized (10 ft wide) corridor, moving at half speed and incurring some penalties. But they could not squeeze through a medium or small sized hallway.

If you are looking for a RAW answer to the extent of allowing no content of any kind not officially handed down by WotC then no. As several others have said, you can squeeze an elephant at half speed through a ten foot wide space assuming headroom, but it is a huge creature whether you want it to be or not. But rules are not the same as content and (outside of organized AL play) even RAW assumes the creation of custom content.

It never specifies in the rules of wildshape that the beasts must always be chosen from entries in the monster manual with their exact, unmodified stat-blocks. It never even references the existence of such a book. It does say on page 6 of the monster manual that a DM should "feel free to tweak an existing creature to make it into something more useful for you" and pages 273-83 of the DMG are all about how to do so.

So long as care is being taken to create a balanced creature, if your DM wants to stat out "young elephant" for you and give it a CR that you can wildshape into then that is not even really in the realm of a homebrew rule. It is how the core materials are intended to be used, as it is content creation for a campaign rather than a rule change.

The polite thing to do would be to offer to create a draft version of the creature and save your DM the work. Don't go crazy with it, but establishing that elephants start as babies and grow into adults in your campaign setting is not exactly going crazy.