1960s family adoption- birth certificate???

Hi all, I have been told that maybe 2 of my cousins maybe my sisters . Supposedly my mum was young in 1960s and gave them to my aunts to raise. My mum died 12 years ago. No one talks in our family but I’d like to know. Where do I start? Will ordering my cousins birth certificates give me evidence? My mum and her sisters obviously have the same maiden name so ansestory websites were no help. Any ideas please?