Suggestions on how to sow seed?

I would like to take a bunch of seeds and broadcast them out all over my garden. Don't want to bury the seed in the existing soil. I'll just let the seeds sprout and grow however they would like. Will not thin them but just let them sort it out among themselves. Maybe I could do seed balls or throw them hard enough they get under the existing soil. Since I want the seeds all over basically every square inch of the garden, digging trenches would not work. Any suggestions on sowing methods?

I like to make use of my bagging lawnmower for certain types of seed sowing. If I have collard or chard or chicory that has gone to seed, with the seed dispersed along long, gangly stalks, then I just lay the dried stalks on the grass and run over them a few times with the lawnmower. Then my lawnmower bag is not merely greens for the compost pile, it is seed enriched mulch to spread anywhere I want those seeds to come up. I've got some nice stands of chicory that really took off after the last good rain.

You don't specify what you're planting, but I think you'll find that many vegetable seeds will not germinate unless they're covered with a thin layer of soil. I guess the evolutionary explanation for this is that some animal disturbance was necessary (or at least could be expected) to allow the seeds to find suitable new homes.

I've been experimenting with broadcasting a thin layer of compost over the scattered seeds, then watering. I can't say that my results have been very promising. I'm starting to think that some amount of soil disturbance really is necessary for vegetable seeds to grow. Maybe it's just breaking up the surface with a hoe or rake and then raking the soil again after sowing. Your mileage may vary. Good luck!

I think seed balls are a great idea for broadcasting.

If you are willing, can you tell us what part of the world you are in? Even just a constant will help. Also, a bit about what sorts of seeds you are planting.
There are lots of different techniques for broadcasting seeds, some work better in different regions and seeds.

Seed balls work because they keep the seeds in close contact with soil (the ball components).
To broadcast seed and have good success, you need a 4 step procedure; 1. rake the space being seeded. 2. spread seed. 3. lightly rake again to insure seed to soil contact. 4. water daily to keep soil moist so seeds will germinate.

I have recently tried to use my hogs for this, what I found out was; I have to let them root up the ground then I have to sequester them away from the seeding area.
The reason I have to do the sequestering is that they will come back and root up all my freshly spread seed because the soil is nice and soft from the watering.
I am putting up cattle panels next time so the hogs can't get in there and undo what I just completed having them help with.

I'm in central Georgia. I'll be spreading leafy greens such as spinach, kale, collards. Got a thousand pounds of vermicompost to use for the seed balls, but seed balls seem time consuming. Need to look up different methods for making the seed balls. Might just use a wheel hoe cultivator, make rows very close together all over the garden, put vermicompost in bottom of rows, drop seed in then cover with compost. Don't really want to spend money on a cultivator though.

Benton: I'll contribute something now that you seem willing to disturb the soil...

How about making a planter out of a piece of metal pipe cut off at a 45 degree angle on the bottom. I do nearly all my planting with things like that.

Tube Seeder

A great way to plant seeds is to first have bare soil spread seeds and then cover with dry tree leaves you can crush the seeds for better germination but if you expect heavy rain or flood or irregation its best to leave the leaves hole as they will stay in place better and protect small seedlings.

I find that I get the best germination on surface broadcasted seed by roughing the soil a bit first, seeding and then mulch with about an inch of ground leaves or grass clippings. Whole leaves are too big, grind em up with the lawnmower first.
This keeps the soil surface constantly just moist enough without without washing seeds into piles as watering does.