No, most farmers leave lambs until the year after they are born to shear them. The exception is some do shear in the autumn, before the weather turns, to stop them having such a full fleece over the winter which obviously gets wet and heavy.
We just cover current year lambs over the summer with fly pour on, to prevent strike. They can regulate their temperature fairly well and sit in the shade if too hot. Depending on when you lamb, there’s not too much wool on them yet, compared to a fully grown sheep with a year’s worth of wool before its shorn.