I'm on a quest to find...

You can get what's called "junior cassettes" that starts at 14T. but that's for road bikes. So they don't go very high.
And there are MTB cassettes that go well past 40 these days.
Those generally require either a special derailer and/or an adapter to drop the derailer down low enough to deal with the biggest sprocket.
You'd have to do some research as to how the cassettes are put together.
It varies between groupsets.
Some use a "spider" or carrier for the bigger sprockets.
Others are merely a stack, separated by spacers.
Those that are merely a stack of sprockets separated by spacers are quite easy to customize.
You'd have to buy both a mtb cassette and a junior cassette, then find a sweet spot where to switch from the junior to the MTB.
But maybe with luck, you can keep the carrier-mounted MTB sprockets amd simply swap in the small half of the junior road cassette w/o getting an unmanageable step in the transition.
What kind of bike do you have, what's your current drivetrain?
It might be overall more sensible to switch to another crankset instead.
Bigger rear or smaller front really doesn't matter as far as rider effort is concerned.

Miche makes cassettes in a broader variety of configurations than most other manufacturers. They also sell kits to dealers so they can build custom cassettes. I've seen dealers advertising this service. Like you, I have no use for 11 tooth cogs except on mountain bikes. I currently have a couple of Miche 12-32 cassettes that I use on my gravel bike wheels. I know that you can order cassettes with 13t starting cogs and I'm pretty sure that you can start with a 14 as well. I'm not sure how many teeth you can get on the low end.