My husband and I are in a 420 sq. ft apartment with a 1 and 3-year old and I think we could make it work with one more kid! The layout isn't awesome, but it does have a huge walk-in closet that we fit a toddler bed and a mini crib into (in an "L" shape). The mini crib was at the foot of our bed for the 1st year of the baby's life, so a third baby will park there if we expand our family. We moved in as students and stayed after having our daughter because the rent was cheap and it was doable with a baby. We renewed our lease again just before baby#2 arrived because of COVID economic uncertainty. We just renewed the lease today for another year, because we were surprised to find that it still adequate. It also gets us that much closer to our financial goals. Our regular monthly expenses are $24,000 per year for a family of 4, thanks in large part to this apartment.
The keys to making it work for us are:
-Remember our why
(I want to have a mid-sized family, stay home with the kids while they're young, live in Mexico for a few years, buy a house in a nature-filled HCOL state near family, and pile up our savings and investments. And I want to get started on those goals during the years my husband is in school and our earnings are low. Keeping our expenses super low was one way to go about it.)
-Keep the end in sight
(We're doing this for a limited time. That makes it an adventure rather than drudgery. I'll have good memories from this place, even if I'll be happy when we move on. It also helps to take it year-by-year)
-Get rid of most of our stuff
(We've become extremely minimalist in order to not feel cramped. There's no way we could fit 4 people + a bunch of stuff. The stuff had to go (that includes excess baby gear). I like the method of figuratively emptying out the entire apartment and bringing back in only the most essential items first. Or dedicating one bookshelf for books, papers, and electronics or one bin for toys and one drawer for art supplies, etc. Then filling the space with the most essential items first and once the space is full, donating the rest of the items. It wasn't until I got extreme about decluttering that the apartment started to feel roomy enough)
-Free up closets by using free-standing wardrobes.
(We have a wardrobe in the entryway for coats, bags and shoes and one in the bedroom for my husband's and I's clothes. Those items used to take up most of the walk-in space. The wardrobes essentially turned our 1 bedroom apartment into a 2 bedroom with space to spare for baby items I'm storing for a possible third baby. I second other's suggestions for hooks, bins on shelves, and under-bed storage.)
See it as a fun challenge.
(I'm always thinking about how we can best use the space. It's like a big puzzle. I get lots of inspiration from others living in tiny spaces (RV's, sailboats, tiny houses, apartments).
It sounds, however, like your situation is more about reconciling being close to family, reaching your FI goals, and concerns for quality of life. If it were me, (and if we're only talking about the expense -and not the income- side of the equation) I would prioritize family and quality of life, and rent something more expensive that had more natural light and less concrete, even if it meant FI plans were delayed due to higher cost of living.