Mulch + Cover Crop… in Spring

I got a little… overzealous with the garden bed as this is the first year I have had total control at my house. I talked to fried who recommended cover crop in the early early spring + mulch. I added a bag of compost, put down some cover crop, and then mulched overtop. Fast forward and now I have starts in the bed with mulch and cover crop growing like crazy. I think I played myself!!! Now what??? How do I mitigate without causing too much harm to the soil? I’d like to practice no till here. I have a few other beds that I didn’t cover crop but mulched and they’re much more manageable.