Nuna make some car seats with totally natural coverings (merino wool, I think) - there is still plastic in the shell of it obviously, but you can avoid plastics in the covers. And I think Besafe make a car seat out of totally recycled plastic. < Never mind, it was just a booster seat, and only the cover.
Another car seat related switch would be to get one which doesn't need the isofix base to strap in with seatbelt, although I have a feeling that rules out the Nuna seats. You could even consider one which does birth - 4 years (rather than buying two separate seats to cover that stage) although I wouldn't recommend birth - 12 because you make compromises in safety with those seats.
You don't necessarily need a pram, you can make do with a sling. Plenty of plastic-free options, woven wraps, stretchy wraps, ring slings and mei tais I would look at.
Co-sleep so you don't need a cot. Go straight to a single bed or mattress on the floor later. Little green sheep do plastic free mattresses in all sizes, I believe. Out of my price range but maybe you'll save on not buying some other things! If you do want a cot, you can easily find all-wood and the cheapest ikea one converts beautifully into a co-sleeper cot if you like that idea. Most of the purpose built co-sleepers are plastic.
Glass or stainless steel bottles and latex teats if you need/decide to use bottles at all. Dummies can be totally latex and one piece (although harder to find). And babies can use ordinary side plates and small bowls right from the start as long as you sit with them to pre empt any throwing. Teaspoons and other small-sized metal cutlery exist. And BLW so they don't need cutlery or plates to begin with! Tripp Trapp (or cheap alternative) is a totally wooden highchair, and often found second hand.
Bath them with you (or dad) rather than getting a baby bath or using a bath support. It's lovely.
There used to be a lovely magazine I liked called The Green Parent with a nice forum as well, that would be a good place to look for more ideas if it still exists.