I should admit that we have a car. So it's not the same, but I can tell you what helps with getting my 5y 3y and baby and all the associated clobber around when we don't use the car.
The children help to carry things from when they first walk. At first it's a couple of muslins in their little life backpack. But we build up and it makes a significant difference. Each child now has a small backpack and a large (for them) backpack.
We also have a beach wagon and a granny style shopping trolley, along with a pull along bag for each bear. They love using them and even the 3y wants to pull along the wagon or shopping trolley.
I carefully plan what to take. And we build up from small trips to more adventurous ones or trips further afield.
The hardest to prepare for is variable weather (if it's rainy all day, for example, we won't need anything to carry the waterproofs in so it's easier). I try to do the trips where there's a lot to take on the days when the weather is likely to be similar all day, and make the most of the minimal-luggage trips on the variable days.
Joining some local eco groups informed me about some better public transport options which I wasn't aware of, such as a bus where you can request the journey you want (with approximate timings and certain restrictions).
Building up the children's stamina (and mine!) now means that if it's an hour or less to walk each part of the journey, we walk it. That can get us to lots of bus stops, to a few railway stations, some shops, half our extra-curriculars, a nature reserve, a few local beauty spots and several friends' houses.
Therefore, with train or bus, it can also get us to some beaches and to our nearest really big city.
I'm building up to cycling more in the hope of getting an electric cargo bike (very hilly area). Places which are ten minutes drive to/through town are already walkable for us. With an electric cargo bike we won't need the car for the nature reserve and friends' houses which are ten minutes by car into the countryside either.
I'm not going to pretend I never use the car or that it isn't really useful. But just as we're gradually using the car less and less, I want to encourage you that you could get further and further afield without one, just one new adventure or experiment at a time.
Oh and I keep a note on my phone for each place/activity of what to take, and update it as needed after each trip. But you might not need that if your memory is better than mine!