They are all different. I transported a rescue bunny to a new owner and he was extremely calm and affectionate.
My own male bunny has been exactly the was you describe running around me licking snuggling etc.
Scared ttie.id bunnies usually get mellow with age.
So to answer your question yes they can be affectionate from day one…but I have only had boys act like this.

Tiie.id is timid spell corrected by my stupid android pad.

I’ve been wondering the same question myself. I have little baby holland lop just three months old, and she’s gotten VERY comfortable and happy in my apartment running around and playing, but I fear so far I’m not getting any real affection and all the attention I get is simply asking/demanding treats and food… I admit I was probably too giving with the “good stuff” right from the start.

All bunnies are different, just like people. Some bunnies take longer to learn to trust and love their person. It also depends a lot on how your bunny was handled/cared for before you got him/her. I strongly suspect my Olivia was abused or at least badly handled before she came to live with me. It took her well over a year to enjoy my pets. Now she can’t get enough!

I got lucky with Cinder, to be honest. Right out of the gate she wasn’t very affectionate, but at least she would circle me and acknowledge my presence even if I wasn’t alpha bunny at the moment. I can’t honestly remember when she “clicked” and started hanging out around me, licking me and giving more of her trust but it comes with time as stated before. Every bun eventually comes around, but it takes a lot of effort. It’s another benefit of owning a rabbit. They’re respect and love isn’t given – it’s EARNED.

Merlin as scars on his ears so very much came from an abusive home. Its taken almost a year for affection – he lets me stroke him but hes pretty much independent. I’m hoping he’ll get more lovey, but i’m happy hes just calm in my company!
Luna was a neglect case, so she has been very scared of everything. but she is very cuddly with merlin. it would be nice to get a cuddle bun tbh! Time will tell.

I’ve found that you can usually get them to like you quickly if you give them lots of attention, and mean it! Lie down on the floor, gently stroke their ears, rub their forehead, try to make them do the happy teeth-grinding. This sounds weird, but it helps if you’re enjoying it too, because they can sense that. Like you know when you’re cuddling with an animal and it feels good for both of you because, I don’t know, maybe your head fits so comfortably into the crook of their neck or something? And you can tell that you both are just loving it (Ugh, this sounds so weird hahaha)? That’s what you want when you’re trying to get a rabbit to like you. You want to be in a comfortable position and perfectly relaxed. I feel like they can tell if you’re not enjoying giving them attention because you’re stiff or something. When I got my older Dutch, it took a month or so because he was my first rabbit and I didn’t know anything. I would just stroke his forehead and rub his nose. We had a slow start. But it took my New Zealand like a day because I knew all the tricks by then!

Batbun:
Bunnies really change behavior over time. Older rabbits can sometime allow more affection than teen bunnies.
They really are like cats in some ways. When they want loving they ask when they do not it cannot be forced.

My boy bunny started loving me within the first week, but the girls are just starting to love me and it’s been 6 months. In my experience boys are more affectionate than girls.

I’ve only had my Jude for 2 months now and he’s almost 5 months old. At first he would let me pet him but even in the beginning he binkied and zoomed around my room. Now if i’m up on my bed with him down below he tries to jump up there with me. When I sit in the floor with him he cuddles and lays in my lap licking my clothes and teeth purrs. If I lean down to his face he licks my face and gives me “kisses”. When I leave the room he hides behind the fan in my room and when I come back jumps out like he’s trying to scare me and zooms around my feet until I pay him attention. I would say he loves me and is very affectionate. I’ve never even had a cat or dog as affectionate as this little boy<3