Should I let newborn sleep at night?

I am planning on asking my pediatrician in few days, but would like to get ideas before that. So, my 2 month old usually feeds every 2.5 hours during day time and at night she does make noises but stays asleep. I can see sue is hungry looking for milk but her eyes are closed. Sometimes if I do not pick her up to feed she would fall back to sleep again and sleep for another 3 hours. I feel bad for for not feeding her but she wasn’t crying. And I am thinking maybe she can be trained to sleep through the night this way. Any suggestions?