Infant Pool

All the floats I've seen online are where the baby is sitting in as they would in a walker. I wonder if theres something in the market where my baby (one year) can rest on his stomach with his head resting on some pillows or attached, and have a place for the arms and legs to move in and out water. Something like this exists?

You can not find something for children that young people do not fully support their bodies. It would be too much responsibility. You can always find a life jacket made for young children (but remember to check the conditions of weight). You can also watch swimsuits with integrated lifejacket, but they require close monitoring due SUPER if the child returns to the back, drowning can happen quickly. We used one of these (link below). Click on "float pool" and get to swim tee trainer. It is for children 18-25 lbs. so make sure your toddler is at least 18 lbs. They also have a life jacket for small children 0-30 lbs.

Any flotation device for a baby is conceived with the intention of keeping them standing with their heads above water. I'd be very surprised if a manufacturer of flotation would take the legal responsibility to design something for the purpose you describe.

If you want to teach your child to swim, you can still do so with or without a flotation device. Responsibility for security lies with you as a parent, but I take my children in the water as they were about 10 months, and even allowing them to dive for a short time just getting used to. They are now 6 and 4, and although I do not allow them in the water without me, they can swim and are very comfortable in the water. The key is to take is slow, be patient and make sure they do not have a bad experience in the water.