Sefiras Haomer

Question

I know that in the past, you've said that your father holds that (without a minyan) one could do Maariv as early as 20 to 30 minutes after shkiah and after shkiah with a minyan. Now, what about for counting the omer? Would I be permitted to count sefirah 20-30 minutes after shkiah or would I have to wait until the 3 stars/45 minutes after shkiah mark? Does it make a difference whether there's a minyan or not for this? Chag Sameach to your entire mishpacha and everyone else.