I posted a couple months ago about a day trip my wife and I took with our 6 week old and dog. Of the great number of things we learned that day, we realized that everyone's bag cannot be a "backpack". I bought myself a new pack late last summer, and bought my wife a matching pack for christmas. This freed up my wife's old BOB for our daughter. The scope of this bag is not TEOTAWKI, but a regional disaster forcing us from our home. Our bags do not include much in the way of shelter, beyond extra clothing, this bag is designed for couch surfing or hotel living until insurance can cover our needs.

The bag is a K3 40L Excursion duffle bag, water resistant with handles on each end and wrap under handles on top, backpack straps, and shoulder strap. Lots of ways to carry it, perfect for this purpose, which I would expect to carry either slung over a shoulder or in the hand. The outside has a ton of daisy chain and a mesh pocket on the front. At this point I keep a notepad and a stylus/pen in this pocket. This notepad isn't write-in-the-rain like my other bags, maybe one day.

Upon opening the main compartment you find a mesh pocket in the lid, and a second smaller mesh pocket is in the side of the bag under the lid flap. An internal waterproof pocket also flips out to the front.
The small side pocket holds the few items for a "survival situation" for my daughter, but this is a fairly limited scope. A reflective blanket (because I already had it), and a small tube of glow bracelets/necklaces. These glow sticks were a trick i stole from a guy I met at a local prepper meetup. His daughter was a fair bit older than mine at the time, but every night he gave her a glow bracelet and necklace. if she wandered away from her parents, it was easy to pick her out of the tree line. Another use for these bracelets (with children) is to mark doorknobs in unfamiliar environments or when the power is out, especially bathroom doors for toilet training aged children.
in the lid pocket I put toiletry and first aid items, this will be expanded in the near future, but primarily infant focused.

Currently
a sleeve of cotton pads,
A small tin of Burt's Bee's Baby Salve (medical salve, diaper cream, all in one product)
Camilia is a pain medication marketed for teething babies, one pouch contains 5 doses in single dose droppers. We've never needed more than two doses in a night.
zip lock bag of examination gloves (can be used for medical procedures or diaper changes if hand washing is not an option.
To be added will be infant toothbrush/toothpaste.
I'm on the lookout for travel sized lotion, bug repellant and sun screen. I pay a bit more for travel sized products that I can keep sealed until needed instead of cycling out product more often when decanting big bottles into travel tubes.
Also pictured, an old winter hat I had which has always been too small for me. Gifted to me by an ex, I didn't throw it away while we were together for obvious reasons, and it just ended up tucked away in boxes of "extra winter gear". Prime candidate for a child's BOB.
And a water bottle my wife bought a few years ago. Packs down small, but only expands to hold 500ml. Great for a young child who only drinks 1-2 ounces a day.
The "internal waterproof pocket" is where I've put food stuffs.

Infants are easy. My wife has breastfed the majority of my daughters food over the past 6 months. There was a period recently where milk supply dropped and my wife was having a hard time keeping up. We used formula for a couple days, these were the leftovers from those days. In the ziplock is a bottle from the system we use daily and a pacifier, with a pacifier clip on the top. We stopped using a pacifier before 4 months old, but I figured it may be useful if we're in a stressful situation and need a quiet child for a few minutes.
The remainder of the bag is filled with this rolled up stadium blanket and three "wet bags".

I'll talk about the wet bags (and cloth diapering) first:
Before my daughter was born, we were pretty enthusiastic about cloth diapering. My wife spent hours researching different designs and systems. Typically, cloth diapering parents invest in a single system, but until you know what system you like, and fit your child, you're stuck either investing in different systems, or rolling the dice in one over the others after labouring over online reviews. We decided to go the multiple system route, just to be sure. My wife did the leg work of locating many of the systems at good prices on Facebook Marketplace. Some we bought new, or bought knock offs from Wish.com. Part of cloth diapering is transporting soiled diapers home without soiling your entire diaper bag. That's where these bags came from, receiving one or two with every purchase of diaper covers, These bags are fairly light, durable and waterproof. For several different reasons over the past 6 months, we have been prevented from going cloth diaper "full time" (our idea for full time was at home only, saving the convenience of disposable for outings). Regardless, these bags serve dual purpose, first to organize things within the BOB, second, in the event of soiled clothing, they can be stored within these bags until they can be laundered.
Professionals estimate 8 diapers per day for a baby, we've never personally hit 8 diapers in a day, but I used that to calculate 24 diapers in a three day bag. I split those 24 diapers into two wet bags, one being slightly larger than the other, has a travel pack of baby wipes. Mine and my wife's BOBs also have the same package of wipes.

The JEEP stadium blanket was a freebie with some sort of promotion at the dealership. It lived in my car for a long time, fleece lined with a poly shell. You don't put babies into car seats wearing bulky winter clothing. Typically, parents pre heat the car, wrap the child in a blanket or poncho to transfer them to the car, and then take that outer layer off within the car. Just a challenge of living in a cold climate. This blanket is a great option for protecting a child from the cold without bundling them into a proper snow suit.
Clothing for an infants bug out bag is probably the biggest challenge, especially in my circumstances. My 6 month old daughter has grown at a rate far outstripping "normal". Roughly one clothing size per month, starting at 0-3month clothes when she was born ... my 6 month old wears clothes sized between 2T and 3T ... two to three year old's clothes. Thank the gods for friends with hand me downs. Since starting her bag, I haven't kept clothes for her, because she has been so unpredictable, and life has been too busy to stay on top of something changing that often. She's finally started to slow down, I think (hope), and I plan to put in two sets of oversized pyjamas. Kids can get away with wearing pyjamas all day. They're comfortable, warm, and even if she outgrows them a little, forgiving. My part of the province has been on lockdown since deciding this would be the best route to go, I should be picking up these PJ sets in the next week or two. One saving grace in this category; when I packed clothes in my wife and my's bags, I did so assuming I might be naked and have to leave. My daughter is only naked at two points in the day, never for extended periods of time, and always with clothes at the ready.

The last (green) bag is for blankets. One muslin blanket, large, light, soft. Two receiving blankets, mid size, bit of weight, bit of warmth. Three walmart tea towels - super absorbent, these were bought in bulk as cloth diaper liners, since cloth diapers haven't worked for us, we have tons of these. They are our default bib and general baby use towel. There's room in this bag still, so it will be where I put the clothes after I pick them up. Depending on space afterwards, I will fill the rest of the way with more white tea towels.
Currently, the bag weighs in at just under 13 pounds.
I'll be sharing my dog's bag, and my wife's and mine soon, but I started with this one because I know it needs the most work. Happy to answer any questions or receive any feedback, I've been prepping for a third of my life, I've been a dad for 6 months, this is where those two overlap. I'll edit the post and pictures as I finish picking up the last few things mentioned. Thanks for looking.