Hi Joel. Welcome to NGA!
Sandy gave the best advice, universally valid advice: more compost is always helpful.
(Things you can do right now)
I would say that any time you have compost, you can lay it down between rows as a kind of fine, short-lasting mulch.
If you don't have compost, and the garden is too large or the budget is too small to buy enough bags of compost, you can do a combination of mulching, top-dressing and sheet composting. It is easier to do than to type: whatever raw materials you might have put into a compost heap, instead layer them on the ground, between you rows and between your plants.
1. This serves as mulch until it decomposes.
2. It is compost after it breaks down.
3. As it breaks down, rain, insects and worms will carry it, or particles of it, down into the soil where worms carry it everywhere and leave it behind them as worm castings.
That layer can be anywhere from 1 inch deep to 6-8 inches deep! Just don't use stuff that packs down so tightly that it slows down the exchange of air between the soil and air. For example, some leaves will pack into a tight, choking mass when wet. Fine coffee grounds might smother the soil if more than 1" thick. (In which case I would scratch the coffee grounds into the top few inches of soil, to keep that layer loose and open. Just don;t stir or till sawdust or small wood chips into the soil. That stimulates soil microbes with excess Carbon. they grow like heck, and suck ALL the Nitrogen out of the soil. Plant roots can't compete with microbes.
High-Carbon things ("browns") make good top-dress-mulch. High-Nitrogen stuff (greens) can be mixed into soil.
I think you get the most benefit from mulch if it is 1-2 inches deep or more. Then it shades the soil from sun and drying wind. In hot weather, it keeps the soil cooler. In cold climates, it keeps the soil a little warmer all night and into the Fall. It keeps weed seeds from "seeing" the light, so they mostly don't germinate. What does germinate has to push through mulch to reach the Sun, so it is already weakened and energy has been diverted from weed roots to weed shoots. Now you can pull those weeds with two fingers instead of a knife, a hoe and dynamite.
You can hunt for and collect raw materials for compost - coffee grounds, manure, green or brown leaves, grass clippings, paper, sawdust, chopped-up yard waste, fruit stand throw-outs, kitchen garbage. Don't worry that there are many books and thousands of Internet articles on "how to make compost". Just pile up whatever you collect and water it if it dries out below the surface layer. If you like to get fancy, or you're in a hurry, mix it up as you add things, or stir it a little every few weeks or months. That's more than enough - the fact is, "if you pile it, it will rot".
I think opinions diverge more after your last fall crop is out of the ground. Also, the answer you hate to hear: "it depends".