I am lazy, I have honed this to a fine art. We have nothing that takes over 30 minutes and most are around 15 minutes prep/cook time.
Chopping veg is a time suck unless you are really good at chopping so I avoid that. Bird's Eye Steam Fresh bags are great for veg as a side, they taste lovely, nothing like soggy frozen veg of old. You can get frozen chopped onions which are just as good as a fresh one though TBH I am fairly quick at chopping onions now. Garlic puree is quicker than crushing cloves. If your DC like mushrooms and courgette these can be left chunky which cuts down on chopping time. Sweet potato roasts nicely in large wedges, doesn't need peeling. Don't peel potatoes unless you need to. Cherry tomatoes roast in a very nice way and sort of go floppy so are less of a choking risk if you have little ones. You can buy bags of ready prepared stir fry veg in supermarkets which is fantastic. Frozen peas are an important staple too. They are small enough to cook quickly so are useful for mixing into things like rice, noodles, mince. I prefer tinned sweetcorn to frozen, but same deal. I tend to use tinned mixed carrots and peas for things like pies, rather than cutting up fresh.
Carbs - buy ready made pastry, ready made pizza dough. You can cook potato waffles in a toaster from frozen. Couscous cooks really quickly and you can mix all sorts into it. Quinoa as well - despite awfully MC reputation :o Rice is quick too if they will eat that. Pasta - if you can stretch to fresh it tastes much nicer and cooks in about 3 minutes but dried is also not too long. Look up the simple Italian ways to make pasta. I found this on pinterest, there are other examples: www.recipetineats.com/quick-easy-pasta-recipes/ Instant noodles are high in salt, but you can also cook them without the flavour packet. They tend to be sticky and stodgy but DC like them. Or just buy dried egg noodles plain and follow cooking instructions. If they like soups and/or sandwiches or continental style breakfast, look at part-baked seeded rolls and things like that, that can be a good way to go wholegrain. Is a bit of a pain to pre-think to bake them, though.
Protein - eggs are a quick source if your DC will eat them. Fish tends to bake very fast and is delicious. Little packets made with foil are great as you can do individual veg depending on what each person likes. Add butter and seasoning and serve with potatoes, rice, couscous or break up and serve over pasta, using the juices that collect in the foil as a sauce. Chop bacon or chicken with (food specific) scissors directly into a pan to save contaminating a chopping board, is also quicker, and strips of chicken or pork or beef cook very quickly. I also do this with chillis to save chillifying everything. Double cream makes a good easy base for lots of sauces - yes, it's high in fat, but that's good for children. I tend to fry off the meat and vegetables, add cream, simmer down, you can add stock to loosen it if you want a thinner sauce, or white wine will add a bit of depth to the flavour if you're happy with adding alcohol. This can make all kinds of things - pasta sauce, pie filling, or something like chicken supreme/stroganoff to serve with rice. If you've accidentally made a curry or tomato based pasta sauce too spicy, add cream to cool it down and add bulk. Minced meat also cooks fast and can be cooked from frozen on a low heat so it defrosts as it cooks, meaning you can buy in bulk when it's reduced and freeze. You have to keep breaking up the block. Also slow cooking fattier meat makes it taste nicer. I avoid things like chops as I find it takes too much prep and bother but thin loin steaks can be fast to do. Chicken breasts are best chopped up for speed but can be done whole in slow cooker or oven as sheet pan (spread breasts/legs/wings, veg, potatoes on oven tray, season. drizzle oil, roast). - this kind of thing www.momology.co/quick-easy-sheet-pan-dinners/
Jarred sauces/packet mixes can be fine, and so are things like sausages, nuggets, frozen pizza - serve alongside some fresh veg and it's not even especially unhealthy. Check salt content but they aren't the devil and can save you time cooking from scratch. If something is too faffy check what the ready made option is like. It doesn't matter if you do serve something very salty, fatty, low in vegetable content etc as long as it's not every day. (And children do need good fats and oils in their diet). Home made is not automatically better than processed.
Slow cooker (prep previous night, leave in fridge, dump contents of bag/tupperware in and switch on in morning) is your friend. Sheet pan dinners are your friend. Batch cooking at the weekend is helpful. A decent wok is excellent :)