This is a long shot, but I made friends with my neighbor, who owned a house with a yard, and he was very much in favor of turning the (mostly dirt) lawn into a garden. We've acquired a lot of soil and cinderblocks on our local Everything is Free page, which we plan to use for a terraced little garden of native flowering plants. We got a bit delayed by life stuff and because I was waiting to see if someone would offer up a pile of pavers (as soon as I buy some I just know someone will) but we'll get back to it soon. We've got a peach tree to plant and I'm researching to see if I can find a used solar panel somewhere to drive a small water feature.

We're in the middle of a heatwave going on over a month here and I have been trying to seed some clover in patchy spots in the lawn and as a living mulch for a few of my garden beds and it has been pretty shitty trying to keep the soil moist to sprout seeds. I would definitely recommend waiting until it has cooled off and there is regular rain maybe? IDK I don't have a green thumb

What kind of seeds? If it's nothing invasive you could always go guerilla gardening.

I usually sprinkle my leftover grain mix' in my town wastelands but I don't look for mesurable result.
I do it when I go for a walk, where I walk and I see that nature is a bit wild. Like in the places that have a bit of wild herbs not cut or remove. I don't care much about the time of the year best to the plant either.

This way, I usually see some flowers from flower mix' the next year. And once I had a few tomato grains that I sprinkle on top of some dried sewer mud and I had actual tomato fruits on it almost every year until the wasteland was repurpose.

Nature does not need much human intervention to grow. But I'm sure that with more care, I could get some better result.

I don't wait for rain, but when I see there's going to be a few days of rain, I try to get some seeds out there before it rains. A few days of rain might give the seeds a good start, and then, you could mulch the seedlings to help them make it to the next rainfall. You could use a handheld tool to cut competing plants like grass and use them as mulch. If you can spend a little time every day or week, then you'll figure out what works.