The aspect ratio isn't a constraint, it's a crop
You don't have to regenerate a square image to fit a wide print zone. You drag a frame. What actually changes between crops is what the design is about.

Same artwork, three shirts. Square-ish and large, tall and narrow, wide and cinematic.
Nothing was regenerated. A frame was dragged, and each crop turned out to be a different design — which is the actually interesting part of this question.
Do I need to match the print zone's ratio?
No. Cropping is a control you have, not a problem you solve beforehand.
A generated image arrives at whatever ratio the model produced — square, portrait, 2:3. It gets fitted into the print zone and you drag a crop frame to choose what's inside it. Regenerating "a wider version" is a step that doesn't need to exist, and it's one of the things this site's own first draft wrongly told people to do.
That's the practical answer. The rest of this is the part worth thinking about.
What changes between crops?
The subject, effectively.
Look at the three above. The wide crop is about a coast in weather — the lighthouse is one element in a horizontal sweep of sea and cloud. The tall crop is about a tower — vertical, solitary, the sea reduced to a base. The large squarish one is about the whole scene.
Same pixels. Three different claims. Cropping is the cheapest editing tool available and it's usually treated as a formality.
Which ratio suits the print zone best?
Something wider than tall, because the zone is.
The statement area is broader than it is deep, so a landscape crop fills it and a tall one arrives smaller — which is a scale cost rather than a rule. A narrow vertical design can absolutely work; it'll just be physically smaller on the garment than you might expect.
Worth deciding on purpose: do you want it big, or do you want it tall? You can't have both.
Should I generate at a specific ratio anyway?
It helps a little, and mostly for composition rather than fit.
An image generated wide tends to be composed wide — the model arranges elements to fill a horizontal frame, which gives you a better wide crop than cropping a square would. Same in reverse for verticals.
So if you already know the design is a horizontal scene, asking for it helps. If you don't know yet, a square gives you the most crops to choose between, and choosing later is usually the better order of operations.
What gets lost in a crop?
Whatever was at the edges, which is why the edges are worth watching.
The classic loss is the bottom of a subject — feet, a base, the ground something is standing on. Compositions that put something meaningful right at the frame edge are the ones that suffer, and that's true of any crop, not just this one.
The practical version: when a design has an element you care about near an edge, check it in the crop frame before ordering rather than assuming it survived.
Can I use the same artwork at more than one ratio?
Yes, and it's an underused way to get more out of one design.
The three shirts above are three products from one piece of artwork. For a set, a series or a group, that's a way to give people variety without designing three things — the same mark treated differently reads as a collection.
It also lets you test which crop people actually respond to, at no cost, because nothing was printed in advance.
Does the back print use the same ratio?
No — the back zone is wider and deeper, so it takes a larger and more square composition.
Which means a design that felt cramped on the front may sit comfortably on the back, and a wide cinematic crop that works on the front might look small there. Front and back are different design problems rather than two copies of one.
How do I get one made?
Bring the image to JustOG or describe the idea. Pick a direction, drag the crop frame until it says what you want, see it composited on the real garment, and it's made to order and shipped.
Designs other people have published are in the shop.
Three shirts, one file. The frame was the design decision.