I am a Naturalized US citizen. I have a baby boy that was born out of wedlock in the Dominican Republic before I was naturalized. My child has a German Passport and entered the US with me on a VWP/ESTA a month ago. I want to apply with forms I-130 & I-485 but now I am scared that he could be deported. I do have sufficient evidence that he is my son. What are the chances of deportation of a baby?
It seems the chances are small, though it might depend on whether there is someone abroad who can take care of the baby.
Most of the information I could find online concerned the deportation of unaccompanied minors, which isn't particularly helpful in your case. I was looking for information about how the US identifies who will care for the child upon arrival in the destination country, but I did not find anything.
The main thing I would worry about if I were you is the presumption of fraud in bringing the child to the US under the visa waiver program (VWP). Entry under the VWP implies an intention to leave the country, and an application to adjust status can be seen as evidence that such an intention was absent at the time of entry, meaning that the application for admission was fraudulent.
See for example Adjustment of Status for Visa Waiver Program Entrants. This discusses the Department of State's 90-day rule (replacing a former 30/60 day rule) in the context of adjusting status. But it's not clear to me whether this is actually a realistic concern for VWP applicants, because the Department of State has nothing to do with the VWP. Their only role in the immigration system is that they issue passports (to US citizens) and visas (to foreigners). But a VWP applicant has neither a US passport nor a US visa.
The 90-day rule is certainly a concern for someone who applied for a B visa (or any other nonimmigrant visa) to enter the US, but I wonder whether the advice to consider this rule after entering under the VWP is simply an overabundance of caution. Still, I wouldn't disregard this advice unless I had an experienced immigration lawyer advising me to do so.
The "proper" course of action would have been to apply for an immigrant visa for your baby while he was outside the US, and then bring him to the US using that visa (at which point he would become a US citizen). You can of course still do that, if there is someone who can care for him outside the US while the application is being processed. But if there are reasons why you do not want to do this, or cannot, it is certainly possible to apply for adjustment of status. There is enough uncertainty about this process, however, that I would not want to do it without having a good lawyer. The potential consequences of a misstep are serious indeed.
Your son is a Immediate Relative of a US Citizen, therefore, he is eligible for an Adjustment of Status - AOS based on IR-1.
There is indeed a 90-day rule mentioned by Phoog that affects your case. Which basically means that applying for AOS within 90 days of entry there is a presumption of fraud.
However, it also matters in this case your intent when you crossed the border. That is, if you had the preconceived intent to avoid the consular processing to bring your child quicker to the US, the AOS will be most likely denied even after past 90 days. The burden of proof is always on the applicant.
Therefore, given that you had no preconceived intent, you may petition for your child.
In regards to deportation, from what you said, your child will not be deported any time soon. He's not even accruing unlawful presence because he is underage: https://www.uscis.gov/legal-resources/unlawful-presence-and-bars-admissibility
All that said, consult with an immigration layer regarding the best approach to your case and the risks of an AOS from VWP (is trickier than from a visa).
I also recommend checking immigration discussion boards online. There are several of them with tons of information.