If you require Financial Aid to attend a college and apply to the same college through Early Decision, it is critical that you submit accurate financial documents in the first place so that the Financial Aid office can make an accurate offer. This is to your advantage. The Early Decision results are sent out along an offer Financial Aid in the same time so that the student can make a decision.
In the event that your student is accepted, you must then decide to accept or reject the Financial Aid offer within a few days. If you accept it, happy ending to all three: the student, the parents and the college. If you reject the offer entirely, you have just wasted everyone's time applying ED. If you want to negotiate for more, you may be asked to provide additional documents. Time is not in your side.
The question is whether you are willing to accept the offer. Every college has a calculator. If you are uncomfortable with an estimated offer from the calculator, Early Decision is not for you.