Both of our boys have been in the pool from very early on (3 months I think) . We used a neoprene waistcoat thing with blocks of polysterene. Start with 8 blocks I think, remove them as they get better (and bigger). Gives them confidence, lets them enjoy it more, and more importantly, gives your arms a rest!
Eldest was swimming without it by the time he was 3 I think.
I view armbands as like bike stabilisers. Learn with them, when you take them off you almost need to start from scratch, waistcoat allows gradual reduction, to the point of wearing the wasitcoat with no floats. I remember my school swimming lessons the policy was to downgrade to a single armband, so you’d roll over in the water!