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No, that will help them to grow back, more vigorously.

You could try a few things, but I would combine multiple things.

The first thing to do will be to pour boiling water over the area. This will kill off most things, immediately. Do this once or twice a day for about 3 days or so.

After you have done this, you can cover the bed with plastic to kill off anything else that survived the water treatment.

Once treatment is done, you can plant into your fresh soil.

Here are some articles that will help:

https://www.gardeningknowhow.com/garden-how-to/projects/how-to-solarize-garden-beds-to-eliminate-garden-pests-in-the-soil.htm

https://www.gardeningknowhow.com/plant-problems/weeds/boiling-water-and-plants.htm

Without knowing what type of grass is invading your flower beds, it's tough to know what will work, however, one way to deter the grass is to dig a trench around the bed and use horticultural vinegar or some other form of grass killer. Perhaps the most effective course would be to dig a trench and pour a concrete barrier between your lawn and garden beds. Here's an article with natural remedies: https://www.gardeningknowhow.com/plant-problems/weeds/how-to-kill-grass-naturally-kill-unwanted-grass-in-your-yard.htm

As far as weed control... Nothing is forever. Weed control will take much diligence and work on your part. These articles will help:

https://www.gardeningknowhow.com/plant-problems/weeds

These articles will help you to reclaim, and design your new garden:

https://www.gardeningknowhow.com/garden-how-to/info/overgrown-landscape-beds.htm

https://www.gardeningknowhow.com/edible/vegetables/vgen/reclaiming-a-vegetable-garden.htm

https://www.gardeningknowhow.com/special/spaces/connecting-the-garden-with-its-surroundings.htm

You have your work cut out for you! It looks like you need machinery to knock down the overgrown material and clear it before killing weeds. I'm not sure a weedeater could handle it.
Below are a few articles that might help get you started. Also, this website has about every garden topic there is, so be sure to tap in with a search when you have a question.

https://www.gardeningknowhow.com/garden-how-to/info/clearing-and-grubbing.htm

https://www.gardeningknowhow.com/garden-how-to/beneficial/using-goats-for-weed-control.htm

https://www.gardeningknowhow.com/composting/basics/composting-basics.htm

https://www.gardeningknowhow.com/ornamental/shrubs/shgen/landscaping-shrubs-for-nearly-any-purpose.htm

https://www.gardeningknowhow.com/garden-how-to/design/lideas/landscape-design-problems.htm

https://www.gardeningknowhow.com/garden-how-to/info/beginners-guide-to-gardening.htm

https://www.gardeningknowhow.com/special/starting/how-to-build-a-flower-bed-starting-a-flower-bed-from-scratch.htm

https://www.gardeningknowhow.com/edible/vegetables/vgen/starting-vegetable-gardens-guide.htm

I would call the landscape company and speak to the manager. I'm sure he will send a crew out right away to properly install the plants under the weed fabric. There should be slits in the fabric for that purpose. As it is the roots do not have enough protection with just mulch covering them and they probably won't make it through the summer.

https://www.gardeningknowhow.com/plant-problems/weeds/weed-barriers-in-gardens.htm

That would be a sedge grass. They will be quite difficult to rid, and if you have flowers that you care about in your garden then you are doing the best thing possible. Hand pulling will be the best way to keep them down, unfortunately.

Here is an article that will help you to kill common weeds in zones 9, 10, and 11:

https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-9-10-11/managing-zone-9-weeds.htm