With my second baby I put the car seat in the seat of the cart, but with my first one I didn't have a car, therefor neither a carseat, I also lived in a building in the 3rd floor and no elevator!
I also didn't have a Target so I mostly buy stuff from small stores in my town which is not like here where some places you can't walk to a store, back in my home town you had a lot of fresh food and some small stores with others (shampoo, paper towel, etc)
a) wait for some body to help me
b) do many small trips
I would put the baby on the stroller then a bag in the back of the stroller then I put there my stuff. Then went I went back to my building I would put the stroller against the wall, take the baby if I had few things I would carry my baby, the stroller and the bag in the stairs, but most of the times I had to leave the stroller downstairs and put the baby in the crib, then run downstairs for the stroller.
This was only until she learn how to walk, then she would walk up the stairs even if that took sooo long, a few times I had to wake her up because it was to heavy, poor little girl, but it was what it needed to be =0(
Then again no wonder why I lost all my baby weight within months, now look at me, I am spoil!! lol.