I got 60 days notice period due to the company's mass layoff, but my baby is due in about a month, can I request the paternity/bonding leave?

... can I request ...

You definitely can. We cannot know if the company will agree to that, considering the many factors (laws, internal rules, business difficulties...), but you do not need to lose hope.

Please remember that remaining calm and professional (and human), you increase your chances of getting what you want. If you go there demanding what you "deserve", things might end up unexpectedly.

I am somewhat optimistic about this because 4 weeks of the 12 are already covered by the notice, so they only need to grand you another 8 weeks. And 2 months should not cause them any terrible discomfort (financial or otherwise) - especially considering that you will not even be there physically.