I have a 4-month nursling so I feel your pain! But eating healthfully is of utmost importance to me, so I've figured out a few tricks. It's ALL about planning and prepping ahead.
I do a lot of work in the kitchen late at night while my husband holds the [sleeping] baby. I can chop up a bunch of veggies and mix up a homemade dip for them (tahini sauce, hummus, bean dip, etc).
Or I'll chop up a whole head of cabbage, grate a bunch of carrots and thin slice onion into a sort of slaw, then dress it (whatever you like) and put it in the fridge to marinate overnight. It's great the next day and you can eat in one handed right out of the bowl, haha.
I also do the same thing with a regular salad - make the whole thing and just leave off the dressing. Then the next day all I have to do is dress it and shovel it in!
You can do this with any easy-to-throw-together cold salad, like potato salad, pasta salad, lentil salad, quinoa and beans, etc - all full of veggie accompaniments of course. Just have a big tub of it in the fridge that you can scoop portions off of.
I make seaweed salads too, same concept, and same as the others they're beter when prepped the night before and left to marinate. Rehydrate wakame seaweed, add cucumber, onion, lemon juice, sesame oil, and sesame seeds.
I cook dinner every night for us, and I try to make extras for leftovers. I love cold leftovers!
Also when I'm making dinner I'll often throw some kale chips in the oven. They'll keep in a tupperware all week and are great for snacking. I go through a few heads of kale a week like this.
Green smoothies assemble pretty quickly if you know what you're doing and have a plan.
One key is just to make sure you have healthy things available. Nuts are great! So is almond/peanut butter on celery/apples. Make sure you have his stuff around and you won't reach for the graham crackers (I don't stock them so as not to be tempted)
Bottom line, You should be able to open your fridge and grab an already-prepped healthy snack, and that means finding some time each day to do your prep work. For me it's late at night, for you it may be early early morning, or when the wee one takes an afternoon nap, or whatever works in your life.
Hope that helps!