The old gentleman that got me hooked on groundhog hunting, 40 years ago, would let them alone until June 1st. He said the young would make it on their own after that. Sometimes I want to go kill some earlier, but I force myself to wait until June.
I had an old buddy who used to say
"The best time to shoot one is when you see one." That's how we did it with woodchucks when I was a kid. We started as soon as the snow was off the fields, and we never let up all summer. They got a break when the hay got too deep to see them, but when the farmers cut hay, we went after them again with a vengeance. Hitting them hard & heavy didn't seem to put the slightest dent in the chuck population.
Even when the hay was too high to hunt the fields, there were always yard & garden chucks. A friend I grew up with was a real chuck-slayer, and we used to go to his grandmother's farm and give them the business. We'd sit watching the vegetable garden in the early mornings, and take them out with the 22. Granny just loved it every time we killed one of the marauders that were terrorizing her garden. As soon as we'd kill one, though, another one would move in and take over - we just couldn't stay ahead of them. Ditto for 'coons in the chicken house. We could shoot one of those about every week and another would show up. I guess that nature always fill a vacuum ……..
We spent the early evening hours walking the edges of the big field, and that was usually good for a couple more chucks every time we did it. That was an all-summer thing, but just like somebody mentioned in a post here, when the hay was about five or six inches tall seemed to be best. Right after the first cutting they seemed to feel a little too exposed, and they got kinda nervous. They would run for the woods for no reason at all, but when the hay grew back up to where they felt like they had a little something to hide in, they would hang around long enough to get shot. There was a rocky area that ran through the middle of Granny's big field, and it was loaded with chucks. Buster's daddy would set up in the shade right behind the barn and shoot them with the 243. Nothing fancy; an old Savage 99. That rifle had the worst trigger I have ever used, but that didn't seem to bother old Raymond. He was VERY hard on the chucks with it. 100-grain red-box Federal "Hi-Shok" was the load, just like he shot deer with. Those bullets really opened up a woodchuck, even a couple hundred yards off the muzzle.