When my little girl was not sitting up on her own, I would haul her (car seat and all) to the grocery store and place her in the cart. If I put her inside the cart, it filled up the entire area; no room for groceries. If I placed her car seat in the front, it always looked unstable, so here is a solution I found that worked quiet nicely.
Put your “little one” in one of those Bumbo Seats, like the one pictured here. It’s sturdy, wipeable and supports their back. Ava began using it around 3 months of age. You can find Bumbo Seats for around $39.95 at Target, Babies R Us or online. Place the seat inside the large area of the cart, sit them down in it, and VIOLA, your infant will be amazed at the new view around them, plus they won’t be sucking on those nasty handle bars they tend to lean on.
Your baby will get tons of oohs and aahhhs and they will be happy that they’re not lying on their back, like business as usual. Necessity is the Mother of Invention. Happy Shopping!