Starting a new bed and would love feedback on my plan!

I live in colorado and have alkaline clay soil. I have a small pollinator garden of mostly natives. Im a beginner and want to attempt an in ground veggie and herb garden with some pollinator plants to mixed in. I am digging up the grass of an approximately 10 x 25 area, it doesn’t grow amazing there but I also haven’t tried to help it.

Once I get all the grass up I was going to till in compost, gypsum and read elemental Sulphur might help? Then top with a few inches of mulch (massive chip drop from a local arborist). I’m hesitant to till but I can get compost for way less than garden soil to fill any holes for veggie starts, and I dont think anything wouls grow with directly sowing seeds without tilling. I have limited funds but am trying my best to attempt not to destroy what soil I have and still make this work, without waiting years to slowly amend the soil. Am I just in a fairy-dream that I can possibly grow veggies in ground here? If I fail miserably I’ll just plant native seeds next year I guess.