Im in NZ and the Plunkett Society and other experts here recommend the time awake for a baby less than 3 months old is only about an hour starting from the beginning of their feed til they are put back to sleep again.
Was wondering also, are you swaddling bub? I know most babies absolutely hate it, but it does help with settling and helping baby sleep in the beginning.
All I know is that with my DD the first few weeks were hell in getting her back to sleep. In some instances she would be awake for 7 hours straight! So know how you feel! I eventually found out that because she was spending a lot of time lying on the floor kicking her legs full on (shes still quite a hypo on the move (or at least wanting to be!) girl at 6 months) she was actually causing her body to release cortisol (stress hormone) which in turn was overstimulating her and stopping her from sleeping even though she was bone tired. As well as making baby feel safe and secure, this is another reason why swaddling is highly recommended for newborn babies.
As soon as I started to swaddle her once an hour was up(ended up half swaddling as she likes her hands near her mouth)and give her her dummy, she would eventually settle and get sleepy. This was sometimes very difficult in that she would grizzle and kick and totally resist her arms and legs being swaddled tightly next to her body. But if I held her tight and restrained her from breaking free I found that she would give in within minutes of fighting. And the fight was by far much shorter and easier to cope with then if she was left to stay awake for 7 hours and then turned into a feral screaming monster in the afternoon (aka arsenic hour)!
Then I would maybe rock her for a bit and sing to her softly while watching for tired signs. Once it was apparent she was ready for sleep, I would place her in her bassinet and in no time at all she would be asleep. I couldn't get over how once I started doing this her sleeping patterns instantly changed for the better!
So maybe...your bubs was like mine in the beginning...extremely active and alert!
Anyway here are the most obvious tired signs and stages in three steps that were explained to me in a way I found to be easy to remember and look for with bubs
1. yawning, jerky movements, clenched fists
2. the vacant/daydreaming, staring into space "lights on but no one home" stare, and
3. eyes drooping and then rolling into back of their heads.
Once stage three is happening, you can pretty much be assured that when you put them down to sleep they will be lights out within minutes, if not straight away!
I found with my bubs that occasionally she would grizzle (not cry) for awhile and fight going to sleep, so every few minutes I would go back in and put her dummy back in, reswaddle if necess (yep they are experts at getting out of them), place her on her side and pat her bottom until she quietened back down and after 2-3 goes at doing this (within 20 mins) she would be asleep!!!
Anyway I know each bub is different, but hopefully some of this helps.