Yes. Gifted funds are acceptable capital provided the gift is genuine, with no obligation to repay, and provided the donor's lawful acquisition of the money can be documented. The evidentiary burden extends to the donor's history, which is the part families rarely anticipate.
The question moves from your records to theirs
Hypothetical example: Hartley is a Callander heating and cooling contractor whose mother has offered a substantial gift toward an EB-5 investment. Capital must be shown to have been lawfully obtained and its path to the enterprise traced. When the money is a gift, both requirements attach to the donor as well as the investor.
For Hartley's mother that means demonstrating how the funds she gave were earned or realized, which in this scenario runs back to a property purchase, its sale, the discharge of any mortgage and the treatment of the proceeds for tax. The gift itself should be recorded in a written instrument confirming that nothing is repayable and no security has been taken, because a disguised loan is not the investor's own capital at risk. Where the donor is elderly, or where records are held by a family accountant, gathering this material takes longer than the investment decision itself, and starting it early is the single most useful piece of preparation.
Establishing early whether the donor will allow her financial history to be examined also matters, since a gift is sometimes withdrawn once that is understood.