I consider this a scheme.
the guy will give you a belt, but you will be a lousy blue belt, easily defeated by any decent white belt, who will only be able to submit terrible white belts, and stand no chances against 90% of normal blue belts. there will be exceptions, of course, but these will be like 10% of the cases, usually people who already have some grappling experience.
a good timing for a blue belt is 6-18 monts, considering you train an average of 3 times a week. but 6 months would be for guys with some grappling experience, who will only need to make adjustments, or phenoms (they are rare, but tehy exist). less than one year would be exceptions, guys who are very dedicated, talented, and athletic (this counts a lot in blue belt level).
average should be between one year and 18 months.