Hi there and congrats on your new addition
My DS is 15 weeks old and his A time is still only an hour, which includes time to wake up, a nappy change, a feed and a burp. There's not much spare change left out of an hour for anything more than a cuddle and a little chat! DS #1 (now a very energetic 22 month old) also had very limited A time probably for the first 6 months of his life. I think I mentioned on another post somewhere that everyone used to joke that they didn't even know the colour of his eyes as they were always shut
You are to be commended for being such great parents already for wanting to interact with your little one and "show him the world" but you'll probably find anything more than a nappy change and a feed at this stage is probably all he can handle before wanting to get back to some serious Z's
For when he can cope with a little more awake time, he'll love lots of cuddles and chats, looking into mum and dad's face from lying on your knee, round-and-round the garden, eyes and ears/mouth and nose, etc. I think the best thing you can do for your baby is to talk to him and to read to him. We used to read to DS1 from when he was about a month old and he is now an avid little bookworm.
Enjoy this time - it really does fly by quickly!