OP: You'll be fine!
It's so refreshing to live simply in a smaller space, so long as that is an ambition of both you and your DP.
We are a family of three (hoping to be four), plus a dog and cat living in 1000 square foot apartment. I love that I can vacuum the whole place using one outlet and be done in twenty minutes!
We have a large open concept living room/kitchen/dining area, which we spend most of our time in when we're home. We have a small bedroom that is DD's that we hardly use at all. She sleeps with us. It's mostly used as a guest room right now. We have a larger master that is our family bedroom.
If we stay here long term and have more kids, then we'll flip the rooms and make the smaller room the family bedroom, with pretty much only a king size bed squished in it, and turn over the master room to the children, especially as we'll be homeschooling and so will use that room as a playroom/classroom.
We have a tiny closet (reach out and touch both sides easily without stretching) that I've made into a super cozy office for me (I'm a writer).
We have a small concrete patio out front that we spent a lot of time on in the summer, playing with water and soap and sidewalk chalk. We have many parks nearby that are busy with other young families who don't have big yards. It's a fabulous way to live!
We also have a busy library nearby, and a free family drop-in space that has lots of the big-ticket items that we don't want to fit into our small home: play kitchen, art easels, sand tables, train table, etc.
I think a vibrant local community with busy, fun parks nearby is essential if you live in a small home with no outside space.
When we had a large house, we spent a lot of money on maintenance and a lot of time on upkeep. This is by far a better way to live. I would, however, LOVE to have a yard and a garden. If we move to a house again, I would love the same square footage, but a big yard!