Help Needed, what is a safe way to rid a garden area and raise beds that are infested with tree of heaven. bought house in 2015. Had no idea what TOH was, and that there was 15-20 huge trees out back (and oh yeah one had gone to seed).. middle of 2016 Had someone come in and take down all the TOH and brushhog a massively overgrown back area. end of 2018 covered a 20 x 40 area with tarps and 2019 built several raised beds. no issues in 2019 or 2020. over the winter of 2020 into 2021 had large herd of deer folded over my fencing and decimating the beds (beds had ends broken - sides pulled down) 2021 year of disaster. I found that I had dozens and dozen of TOH now growing thru out the garden and beds. Advice I was given just keep pulling them out it, and they will go away. TRUST ME that makes it worse. Just like, keep mowing them and they will go away. This year I did not plant my garden because it and the areas surrounding the garden have become over run with hundreds. Just one tree of heaven will spit out 3 hundred thousand seeds each year. So back to the question when can I use to kill the TOH in my garden area that will not poison stuff I am growing or future areas I want to grow in. Picture included is the site next to the garden (where I was going to expand the garden). Picture does not do justice on how many there are coming up this year. (this is the area I wanted to expand to)

I have no answer but am very sympathetic. I think they also sucker a lot from the root system. If some are suckers, then poisoning those, by specifically treating just those leaves and stems, could maybe knock back the mature trees.
https://extension.psu.edu/tree....
Are any mature trees still there? Are there any around your property adding new seed load?

We took care of the mature trees. There are a lot of suckers and you can follow the lines out. Some of the further out ones I have hit with woody plant killer. I am trying to find something to use that is safe for in the garden. I wish I could burn them to the ground, But that, like everything else will trigger a defense mode and send out more. I have read and watched - but everything is do not use near veggies

I swear, just looking at them.... Triggers their defense mode and sends out new shoots.

I feel your pain, mostly because I live your pain. TOH are the worst noxious weed I've ever dealt with. (My husband would argue oak tree seedlings are running a close second though) Unless the tree removal guys poisoned the stumps, you are dealing with very extensive, very enthusiastic root systems from 15 or 20 trees. The seedlings are easily dealt with by pulling or spraying them with roundup but the suckers... Your best bet is spot spray them with brush killer. I keep an old 409 spray bottle of full strength brush killer on hand for just this purpose. The only way to kill them is by stressing the roots. "Just keep pulling them" would be good advice with any other tree but for TOH, that's encouragement. Good Luck!

Concrete pad and new soil.
It will be an eternal struggle since any piece of root left in the soil will sprout from both ends and sometimes in the middle. Keep full strength glyphosate and or trichlopyr handy to apply to every sprout you see. Neither one will last in the soil to affect veggies.