We have issues with this too

Our budget is between $300 to $500 a month depending on what yearly bills are due that month. We live in Southern Cali where we are a family of 6 with 2 very big male eaters (DH is 6’4 and 270) 4 cats and 3 dogs. Also one in diapers so we use cloth diapers which saves a ton and is so easy to use.
I use coupons, loss leaders, clearance racks and try to make as much from scratch as I can that I cannot get cheaper with coupons. It always seems to be a balancing game. I had been sick the last few years ending in 2 surgeries last July. I am getting my strength back so we are back to growing some of our food. Just planted some carrots today.
I know people call those that use a lot of coupons and store a lot hoarders but it really makes a big difference when you do not have to worry if the kids will be able to eat. When there are great coupons I try to get as many as I can and stockpile all I can. Last couple of months there was a $1 off 1 Progresso soup coupon. I have about 60 cans ranging from zero to .28 each. We tend not to eat a lot of canned soup so that could last us a year. Also Walmart gives overages on coupons so when it is a coupon where the item is priced less then the coupon I shop there. Birdeye recipe ready is a good example. They range from $1 to $1.99 but there are coupons $1.50 on 1 and $1 on 1 so a lot of free and very cheap veggies for the freezer