Just existing as a first time parent. I have a huge amount of respect for anyone that has two or more children, because one is already stretching me to my limits. To get anything accomplished requires stealing time from something else. So over time, everything is in a state of being half-assed, overdue, or forgotten.
Two weeks truly isn’t enough. I know it’s not standard everywhere, but 3 months ought to be the minimum. The first 3 months of an infant’s life is a huge learning curve that requires lots of time and attention. If you are able to split parenting duties, it will make the whole experience a lot more manageable and enjoyable.
Since it sounds like your company doesn’t have a well defined policy, try asking your hr for a longer paternity leave. It’s way too common for paternity leave to be short changed, or for fathers to opt for shorter leave.