That "the area gets little sun" means you will have the baldest of comb-overs. If too little light, you won't achieve a barefoot lawn, even with weeds, unless you can get the right, low-light tolerant groundcovery weed going.

Do the trees form a dense canopy? Some grasses grow in dappled shade but I don't know one that will grow in total shade all day long. I'm no expert so I hope such a grass does exist; a lot of problems would be solved.

If you like the trees, find alternatives to lush grass that you can live with. If you have to have lush grass, lose some trees. Even if you do canopy thinning to let more light in you'll only get 3-5 years before you need to do it again, and if they don't know what they're doing, a bad thinning job makes the tree more susceptible to wind damage.

Can we have a photo taken on a sunny day?

I doubt you will get much grass to grow in that location. Even the most shade tolerant cool season turf grasses (what a WI lawn is comprised of) need at least 4 hours of sun daily to thrive. And that's ignoring the competition the tree roots in that area would provide. Even if you do get it to germinate, it will likely be more bare and patchy than would a lawn grown under better conditions........and not exactly friendly to bare feet :-))

It's not a grass-growing area. It's a mulch, weed, paving or groundcover area.

I agree that grass isn’t going to work in this area. What is your goal for use? If we know how you want to use it, suggestions can be made that may work.

I agree with Chanabelle. However, if you want to try seed give it a go. All you have to lose is the money. The package will say shady lawn mix or something like that. Check Youtube for advice on spreading the seed. Would you consider artificial grass?

Surface the rectangular central area with cedar play chips. You could also use sand instead, but if there are ever any free roaming house cats around they are likely to poop in it.

Grass is not gonna grow under the shade of big trees. Period. Save your money - grass seed is not cheap. And YouTube is no way to learn how to do any sort of gardening, especially prepping for and spreading grass seed properly. And there is a huge amount of prep and cost involved in the installation of artificial turf. Once in, you're good to go but it costs $$ to get there.

Embothrium has the best idea - define an area, put up some sort of boundary and fill with playground chips. Or shredded rubber mulch. I would probably skip the sand as even if the neighborhood cats avoided it, it is easily tracked indoors and can wreak havoc with wood floors.

There are certainly hacks on youtube, but there are some good sources as well. Like the University of Minnesota https://youtu.be/CNJVbZ7hT8k

Not shredded rubber mulch for a kid surface from my perspective. Who knows what chemicals are in old shredded tires. I would go for Embo’s suggestion for the play area. Other areas can be mulched and/or be planted in shade tolerant low growing plants such as one of the shorter shade tolerant sedges, which look grass, but don’t look good with mowing IMO or hosta or one of the spreading ferns. Plant fairly densely, mulch until filled in, and keep them weeded (not difficult if you attend to it while any weeds are small.)

Or as others have said, remove trees, but this is likely an expensive strategy.

Wood chips or mulch.

If you are looking for a get-me-by, temporary solution that serves partially as paving, and looks is not an issue, some people use used wall-to-wall carpeting that has been removed from a carpet install job. Often, it is used upside down. It keeps weeds down, smooths things out and can last a few years.

I would not recommend carpet. We had to remove some put down by the PO when we moved in, and it was without a doubt the most disgusting thing I have ever done gardening: heavy, wet, and simply oozing with mildew. If you choose to use carpet, use one meant for outdoors. I still find loops of carpet fibers in my garden.

Carpet made from natural fibers is fine. It just decomposes like any other mulch.

Admittedly, I have not used it or had to pull it up myself. I've seen people use it for several years actually, especially as paths, but in same cases, areas. And it seemed to hold up fairly well for its use. Certainly better than trudging through mud. It might be that it's something you'd take out under certain weather conditions. And maybe even with some kind of equipment or hired help. I'm not recommending it for a first order use, but as a stop-gap solution. I think carpet of all natural fibers would last too short a time, decomposing under foot. Also, if wool it would smell bad. Cotton would take forever to dry.