I agree with Attorney Eichorn regarding the individualized nature of each case. I suggest discussing your situation with an attorney, in person. The process for DACA results in only a temporary way to remain in the US. Permanent residency is much better. The application fees are not really much more.
To prove you have been present in the US you can use affidavits from family or friends, letters from your child's doctor showing appointments, receipts, traffic tickets, appointments of your own. An attorney can help you with this.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
Proving physical presence is a very individualized matter. It's best to discuss with counsel and in person. An experienced attorney will know how to take your life and best document it. However, we need to get to know the person and it takes a bit more than a post on a message board to really be able to help.
With that said, you haven't indicated how you entered the U.S. (with or without a visa) and how old you are and your education level. Those factors and more will play into how to handle your engagement with USCIS to get either DACA or status or both (if appropriate).
I agree with Mr. Einhorn - DACA should only be used as a fall-back if there are issues with your AoS. If you entered legally and married to a US citizen your first concern should be completing and submitting an Application for Adjustment of Status. Please contact a qualified and experienced immigration attorney here in North DFW for a consultation to make sure you are following the path that is best for you. My principal office is in Plano on 75 and Park just north of the George Bush and 75N. Feel free to contact me or any of my colleagues in the area for assistance.
Please remember this is not official legal advice, and this is no way establishes an attorney-client relationship. For a free 15 minute phone consultation please call 972-638-7207.