Lydia De Jorge Mar 23, 2020:

Possibly the child kicks a lot and so the father feels he has very strong legs.

Tony M Mar 23, 2020:

@ Asker Normally, this kind of expression would mean 'the legs he uses for walking' — but obviously at just 5 weeks, he's a long way from walking yet!
Perhaps the father means from the movements the infant is making, it already looks as though he is trying to walk?
Cf. expressions like "put my thinking cap on" and "has found his sea legs" (both relatively figurative) — or of course "his climbing boots", in that instance, wholly literal.