It was my 'new boyfriend's' birthday a month after we met - he was 24. He'd had hardly any cards or gifts from anyone, since he was 15-16, only his parents, as he was from a big family, and most of the extended family stopped buying for people when they hit 16.
He'd had 3 girlfriends before me (a one year relationship, a 10 month one, and a 7 month one.) Last one finished with him 6 months before I met him, (the week after her birthday, after she had had loads of gifts off him!)
He had treated all 3 of them to lots of gifts and treats and lovely stuff at Christmas, and he had never had fuck-all from them, not even a box of maltesers.
I didn't know this at the time.... so anyway...
I got him a nice card, some choccies, a bottle of wine, and a hardback book on a specific thing he was interested in - say old cars for example - that I picked up from a shop in Manchester.
I came to his house so we could go to the pub for a drink, and his mother asked me in, and I handed the gifts over. He just looked at his mother, and she looked at him, and there was silence.
I wondered what I had done wrong, and I said 'is everything OK?' with a 
kind of look...
He took the parcels and opened them, and his eyes lit up when he saw the book, and he was chuffed with the wine and choccies.
His mother said 'how lovely Mabel, that's very kind.. and gave me a hug.
As I said, I didn't know at the time, but I was the first girlfriend to buy him anything, and the others had always just taken from him. And that was actually the thing that sealed our relationship I think. He AND his mother - and father too - knew from the very start that this was the girl they wanted their boy to marry. And HE was over the moon at getting some gifts, and said (later on,) that that was the moment he knew I was 'the one.'
All I did was buy a few gifts - not much money's worth - like I always have for loads of people for their birthday/Christmas... And yet he and his family thought the world of me for it, and that was the start of a long term relationship with the man I went on to marry and have a family with. (And am still with 30 years later...)
Don't know why I just told you all that!!! It just kind of felt relevant, as it is KIND of similar to you @OldBaggage You haven't know your man long, and are afraid to do anything that is 'too familiar,' but it could work out great.
As a few people have said, maybe your new man doesn't have many people to celebrate with, and is a bit lonely. You just never know.
I am not sure you sound sure about him though. I was quite sure about mine... I really liked him. Still do! (Love him actually!)