I came across an amazing scene while walking by a lake near my home in the Chicago suburbs earlier this month. There were six baby swans (cygnets)...and they allowed me to get quite close. I also saw ten baby geese (goslings) while at the lake.
These swans were about a week old and so small that one could easily fit in your hand. The mother and father swans, on the other hand, are massive and quite intimidating!
Most of these images were captured from a distance of 9 or 10 feet. The swans were comfortable with me being at that distance as long as I stayed very low to the ground and kept relatively still.