My 5 year old kid just received his social security number. I'm claiming child tax credit for him this year. Can I claim this for previous years by amending?

My 5 year old son is living with me all these years. As he is not a citizen rather has become a permanent resident (with Green Card), he received his social security just lately. I know that I will be able to claim child tax credit for him for this year (2016) tax filing. But what about the previous years when he had not social security and so I couldn't claim any child tax credit at that time. Now can I do amended filling for claiming child tax credit for those previous years? If so then how many years I will be able to claim, because he's living with me since 2013?

Thanks