Thanks for sharing that question about the weed in your garden. After a fair bit of looking, I believe that this particular weed is the Palmleaf morning-glory (Ipomoea wrightii) there are other varieties of morning glory, but this one stands out because of its "V" shaped leaves. It is classified as invasive, but I'm afraid that there is not much more information I could gather about it.
At this point in time, I suggest trying to track the weeds root stem and see if it travels just below the soil surface. I can only recommend manual removal at this point and staying vigilant to make sure that it does not get out of control.
If you have any other questions we can help with, please let us know.
Morning glory vines of all types will produce an abundance of seeds so it is possible that your 'crop' has grown from wind-borne seeds.
Hand removal is you only option if you do not want to use chemicals. Before vegies are planted or sown, you could use boiling water - pour it over seedlings and they will quickly turn up their toes.
Adding more mulch would not be a great i9dea, as the thicker the mulch, the harder it is for water to penetrate down into the soil beneath. Plus, over summer as mulch starts to break down, it can form an impervious layer that prevents moisture soaking in at all.
Good afternoon @hetas I agree with Eric and Noelle, it’s best to pull out by hand as soon as you see them pop up.