I helped run a swim school for about 4 years (probably was the same Emler) and have taught babies to adults. In terms of progress you’ll see quite a large jump when you put your eyes in the water for the first time just from having correct body positioning. Think awkwardly doggy paddling with your head up vs just kicking with your eyes in to get an idea of body position. After that you’re not really going to see that same large “jump” in progress again. From there it’s smaller milestones from repetition and training your muscles to move in a way they aren’t used to. The first things I recommend as an adult learning is how to float on your back just to recenter yourself and how to stand up should you lose your footing. Keep practicing the more pool time you can get the better. Formal lessons help due to having someone to give you feedback but they aren’t required.