Easter eggs have always been gifts from people for us. We do an egg hunt, set up by people.
I did have a lovely book as a child about the Easter Bunny bunnies, there was more than one) delivering eggs to children. I enjoyed the story but didn't think the bunny was 'real like Santa'.
The Easter Bunny is a hare - which are native to Britain and Europe - and hares getting horny, as well as eggs, are symbol of fertility, new life and Spring and have been for millennia. We all know that, surely?
Just think about the similarity between the pagan goddess name Ostara / Eostre, oestrus and Easter.
A quick click on Wikipedia tells me 'Ēostre is attested solely by Bede in his 8th-century work The Reckoning of Time, where Bede states that during Ēosturmōnaþ (the equivalent of April), pagan Anglo-Saxons had held feasts in Ēostre's honour, but that this tradition had died out by his time, replaced by the Christian Paschal month, a celebration of the resurrection of Jesus.'
So if St Bede says the pagan version came first... are there really present day Christians who'd dispute that?
I did have a strange discussion recently when I referred to the Easter Bunny as 'she' and someone 'corrected' me and claimed he is male. Seemed more likely to me that a symbol of fertility, connected with oestrus and delivering eggs would be female.