You need to find a dc-dc boost converter capable of more than 6A. 7.5 to 10A would be best. Note that you'll need to ensure it starts at 2.5V -- some may not.
If you went to design one, start by looking for a chip that satisfies these requirements (possibly using an external switching element).
A problem you may face is that a switching MOSFET may require a Vgs higher than 2.5V. a possible solution is a separate boost converter to create the supply rail for your main boost converter.