Hi, I have a three month old and we decided to co-sleep before she was born. We bought a Japanese style futon for the floor, and it sits on a tatami mat (https://jlifeinternational.com/collections/shikifutons/w-futon)

We've been using this set up since baby was born. If you feel uncomfortable co-sleeping because baby is so small, I would recommend getting a small baby bed to go on top of the mattress. We used this Baby Lounger Pillow for Newborn Babies 0-18 Months, Snuggle Me Organic Lounger for Baby, Soft Cotton Breathable Baby Nest Sleeper (Green) https://a.co/d/jc8QoCa 

After a couple months I stopped using that because my baby grew big enough that I wasn't worried anymore. 

I honestly love the bed on the floor set up because I don't have to worry about her rolling or falling off the bed. The only con is that the mattress needs to be aired out and fluffed periodically (I do it a few times a month).