My oldest started in a school that used very traditional methods (first learn legs then add arms, start by dry swimming on land and move to water, and so on), and she took the course over and over without progressing. For unrelated reasons, we switched schools, and the new school focused on just spending time in water, running in shallow water, floating, dipping your head under water as part of games, and so on.
They had something they called "playing dolphins" where they would stand in waist-deep water, jump forward, and glide as far as they could before standing up again. She only needed one round of that course before she could advance to swimming for real. I suggest spending time just getting them used to water, getting splashed in the face, or playing with floating or sinking toys in waist-deep water, to quickly get over any blocking fear of water. I liked how the new school didn't even attempt to introduce real strokes at the beginner level, but instead gave the kids confidence in their own abilities to move in water.