Restore native pasture after tilling

We recently moved on a 5 acre property in the foothills of the Central California Sierra Nevada. The previous owner tilled a large area (at least 3 acres of the land), which disrupted the native grass and caused a lot if weeds to take over. I'm assuming he did it for fire control and didn't want to keep mowing it, without realizing how tall the weeds would get. I'm very much hoping to get the native grass to grow back that is all around us in the hills and on the rest of the property. I spend the last several weeks pulling the tall weeds with my hands (to the amusement of my neighbors in sure). Now what I mainly have left is a lot of goat heads / puncturevine with some sparse grass trying to fill in here and there, but wide areas with no grass at all, mostly dirt and goatheads. I haven't started pulling the goatheads,  because doing so in this area seems overwhelming even compared to all the weed pulling I've already done, and I read is likely have to keep pulling them many times to make any difference. I read about goathead weevils with mixed reviews and can't seem to find them online anyway. Flame torch is out of the question as I don't want to burn the neighborhood down. I'd like to avoid spraying if I can, but I'd also really like to get rid of these goatheads. If I manage to get rid of the goatheads and keep the other weeds controlled, will the native grass just naturally fill back in? Any input? Thank you!
In case it's relevant, the reasons I want to get rid of them are:
- they are painful and potentially harmful to our dogs and possible other future animals
- they interfere with the native grass I'd like to restore
- I ultimately hope to leave that part of the land relatively wild with native pasture/meadow or possibly put a very small number of animals in it to graze
- they are not native and while they help with erosion control,  the native grass will do the same thing and much more.

Edit: upon Anne's suggestion, I'm adding some photos of the native grass with the tilled/weedy pasture in the background.

Goathead, Tribulus terrestris is an annual plant so keep it mowed short so it cannot go to seed.

My other suggestion would be to over-seed the area with a native grass that will choke out the Tribulus terrestris.

Since you say "other future animals" I would suggest picking a native grass that is good for animal fodder.

It will be interesting to hear other folks' ideas.

There was another thread around here that mentioned goathead grows in dry soil where there is little competition with other plants. Are you able to do any watering to encourage other grasses and plants to move in?

Here's the thread:

https://permies.com/t/69711/goathead-control

They also mention that grabbing and pulling them out is likely what you'll need to do, but that after rains (or maybe after a watering?) the entire plant can come out of the soil - provided it's a small one.

Best of success to you on this...!

Thanks, Anne. Our native grass is actually great for animal pastures. These hills can be great grazing land despite the dry and hot climate. I'm not sure if I could find seeds for it, though. To be honest, I don't even know exactly what the grass is called. I guess that is something I need to find out.

Maybe post a picture of the grass leaves and seedhead for identification.

The folks on the forum are good at that.

I have a native seed company that is in my area that sends me their catalog that I use for id's.

Thanks again,  Anne, I just added some photos. I don't have a lot of the tall native grass right now,  because where the grass is intact near the house, we had to now it down due to fire hazard. I'm thinking it might be California Oatgrass. I'll try to get a better photo tomorrow morning during my walk in an area where the grass was allowed to be undisturbed.

Hans, I feel the ID of your grass is correct.

Since it is a bunch type grass to get it to choke out the goathead the seeds would be sown heavily to create a thick mat.

I would stop pulling things out and start mowing them instead, with my goal being to keep as much organic matter as possible on those dried-out barren looking areas.  The more organic matter you can get on there, the more successfully you will be getting good things growing.  I don't think you would even need to plant, since you have natives going to seed close by.  If you can afford seed, that will definitely speed things along.  Personally, my goal would be building back the damaged soil while letting anything at all that wants to grow, grow, at least at first.  The more things you get growing and the better the soil gets, the more the good things take over and the bad guys die off.  That has been my experience anyway.  Most weeds seem to hate being mowed, and most grasses don't mind.

Thank you,  Trace, I generally agree with mowing, but in the case of goatheads that's almost impossible,  since they grow so low to the ground and I already have a crazy amount of goathead seeds just waiting to grow or to get sick in someone's foot 😪

Lots of experience with goatheads! I've been on 20 acres for 16 years, which was raw/ relatively undisturbed when we bought it. The goatheads showed up in year three when we had a load of gravel delivered, and they have never gone away. They also come in on tires. BUT every single summer when they first show up it's part of my routine to take a 5 gal bucket or molasses tub around to collect them. Just a bit every day or so, especially when wet, and they don't get out of control. That's with them not having been here to start.  In contrast, a friend bought 1 acre in town covered in goatheads, and he combo pulled some and burned some, AND THEN walked his whole property bits at a time with dollar store flip flops and a bucket, in baby steps to collect the seeds on the soles and scrape them into the bucket. Repeat a thousand times.  

I've also known people to drag carpet that is intended to be thrown away, to pick up the seeds.... this is still after pulling or burning.

They are so ubiquitous, by the way, that our local pickup ultimate frisbee team is named the Goatheads, as the field they play on is (like most grassy areas in my small town) host to them.

I wish you the best.

Jesse, thank you so much for your reply. Unfortunately,  you are only confirming what I suspected: that our struggle with goatheads will never really end. 😔  I have been outside pulling goatheads every day, anywhere from a few minutes to an hour. I'm prioritizing the green plants that are still growing. After that I suppose before the rain arrives I'll start over and try to scoop up more of the dry seeds that are unfortunately everywhere. I might even try the flip flop method 😆
Fortunately I can be very persistent, so hopefully I can at least reduce them a bit year by year and allow the grass to start filling in little by little. As long as I can see things moving into the right direction, I will continue 👍

Hans, take heart. You WILL have to get ahead of them every year, but after your initial big effort they are unlikely to ever be as bad as they are now.  You also want to look at drainage.... do you have uphill neighbors they may regularly come from? If so, can you build any kind of collection, like a berm that will contain them in an uphill swale, so your effort will be restricted there? Since even they do compete with each other for space, it's not so much a matter of how many seeds are out there but how much area they might take over, and if you can minimize that total area, your work will be less in the future. (This attention is more for after you get after them this year, but you might be thinking about it as you're pulling, since you have the mental time.)

Also... seeing that all roommates (including furry ones) remove them from their feet before entering will make for grateful indoor bare feet. I have a stroke-recovering spouse who does not do that well because he's not flexible, and ouch! those surprises.... worse than a Lego.

Thanks, Jesse, for the glimmer of hope Lol.
I'm actually not sure where they originally came from. All our immediate neighbors have intact pasture grasses and I'm not really seeing goatheads in their pastures. Maybe they came in on the tractor that was used to till the soil.