I'm not an expert, but I can share my personal experiences. I put my son, who is now 6, through numerous swim classes when he was and infant and toddler. I started with group mommy & me classes. The only thing it taught was how I can handle a child in the water. Later, when he was 3, I put him in Red Cross style group classes over and over again. He learned nothing and hated it. I complained to the director of the swim school who told me that children don't have coordination to do multiple functions, such as kick, paddle, and breath, until they are 5 years old. I was frustrated and pulled him out. I felt the time I was investing was wasted and, although the classes were inexpensive, the money was a waste too.
Then I had a scare. A playgroup friend who had a pool chose to host a swimming playgroup. I had a newborn and my mommy friends promised to watch my son in the pool while I nursed. They were well aware that my son could not swim. However, my son was confident in the shallow end of pools where he could touch the bottom and jumped in. That's was swimming lessons did for him, gave him confidence in the water without the skill of swimming. My mommy friends did not realize how deep the shallow end was in this pool and my son could not touch bottom and keep his head above the surface. I had to jump in with my clothes on to pull my son out.
The strange thing was that there were 3 other 3-year-olds who could swim. All of them had pools at their own homes and had taken private lessons at a swim safe school where they first teach children, including young babies, how to roll over and float before teaching strokes. They had been swim safe since a young age and swimming (doggy paddling) since 2.
I put my son in one of those private lessons. I had steered away from them because of the cost. However, my son was swim safe - able to roll in float - within a month and a decent swimmer in less than 6 months. I feel the money was well worth it and it was costing me a lot more in time and money the other way.
I now have my daughter, who is 3, in a similar kind of swim school. She has learned so much in a short time that I'm amazed. And, in both cases, this style of teaching gave me comfort knowing that my children would be safe at a swimming pool.
However, to answer your question, I have seen infants as young as 4 months old benefit from these private swim lessons. They are able to learn early how to roll over and float. And, they can stay afloat for hours. From my observations, their progress is slower than an older child, but they do learn.
I highly recommend a swim safe school at an infant age (before they're crawling) if you have a pool in your home. I chose to start my daughter at 3-years-old, but it has taken her less than 4 months to learn to confidently float, hold her breath, and perform some strokes. She can swim, not well, but swim non-the-less.