I'll try and do this in steps, as it needs some possibly hidden parts to it.
Create your two text layers. I used the character panel to increase the vertical height to 180%. I'm using LTC Square Face.
This bit is tricky, so read carefully.
Ctrl T (Free Transform)
Right click and choose Warp
Position the cursor just slightly inside the centre at the bottom of the bounding box, and Ctrl click to add a micro point.
Before. Note the Warp handles. There is no handle in the middle of the lower edge of the bounding box.
After.
Hold down Ctrl. Hover in the middle of the bounding box. You'll see a tiny box with a plus sign in it. Click and you have a new handle/point
This is where you can mess up. You need to hold down the Alt key and click on the new handle.
Drag down to distort
Hold down alt and reposition the central handles (my red highlight).
After moving the first, click on the center handle and the other point will show.
Alt drag that handle. If moving one of those points affects the other, then undo and try again while holding down Alt.
Try to keep those handles symmetrical, and the vertical, handle (my yellow highlight) vertical.
You can adjust lower corner points (my majenta handles) to exagerate the distortion. No need to use Alt for these.
OK that and copy it (Ctrl J)
Go Filter > Noise > Add noise. Make it Monocrome, and go heavy on the strength. Because the layer is a Smart Object you can adjust this as often as you like.
Use the Smart Object mask to hide the noise where needed. Use Mask Properties to feather if that helps.
Add a layer mask to the layer (separate from the Smart Object Mask) and use that to fade the lower edge of the text.
I am just doing this very roughly showing you the tools. You'll obviously design to your taste.
OK, let's look at another way to add that noise. I think this is better as it gives you way more options.
Search for a 'noise texture' and clip it to the text smart object.
You can sharpen, change size, invert etc. etc. to fine tune the noise with this method.
You'll need to add a layer mask to this layer. I've done that, but left it reveal all so you can see the texture.
Does this give you something to work with? The text will remain sharp, and can be edited. (Font, spelling etc.)
If you use a t-shirt with folds as is the case here, you'll need to use a Displacement Map to shape it to follow the folds, but that's a whole other post, and I'm hungry.
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