However, your baby can go swimming at any time from birth, although most baby swimming classes start at six weeks. If you're keen for your baby to be introduced to swimming before he is six weeks old, your partner or someone else can take him to a warm, baby pool.e may also be put off by all the noise and activity. Most babies up to six months of age can actually swim, with your help, of course! If you start early you can take advantage of your baby's natural ability to do basic strokes.