Whatever you do, from the voice of experience, if the mother has shown to not be trustworthy, do not restart any relationship with the mother of the child; women often use the child to keep the father around in the 1st or even 2nd year of a child, under the guise of building a family, even if not interested in a long term relationship. (it is usually a waste of time)
As for being a father, while it does seem problematic right now, it can be quite traumatic losing a child. You might get second thoughts later on, or years later after giving up on a son.
On top of that, having a child early on life will mean you will also be relieved of that responsibility early on life, with the added benefit of having your parents around.
I would think about making the DNA test and possibly keeping the kid if the mother does not want it.
Talk both with a lawyer and with your parents.