Deductions & credits

I am in pretty much the same situation being the grandparent of a child whom we have been caring for most of the year.  Is there some way to claim him as a dependent before actually filing my tax return?  If I need to wait until receiving all my 1099's etc, I generally can't file till sometime in March.  His mother, who has not cared for him at all, will likely file earlier and claim him as a dependent.  Can I file an "estimated" return earlier and replace it with a correct amended return later?
Also, the same thing happened last year (2016).  I didn't claim him since his mother had already claimed him by the time that I filed.  Can I still file an amended return by mail for 2016, claiming my grandson as a dependent?