Froome started the 2011 Vuelta with a total of 688 CQ points accumulated throughout his career.
Damiano Cunego had scored 685 CQ points in his career when he started the 2004 Giro, which he won.
When Froome actually won his first GT on the road he had 4303 CQ points to his name pre-race, so in terms of being an un-asterisked GT winner with a low CQ points tally, he is beaten by quite a number of riders. Most notably Aitor Gonzalez, who comes closest to Cunego in this respect by starting the 2002 Vuelta with a total of 1327 CQ points.
Froome is also not the GT podium finisher with the lowest amount of CQ points. Aru had 629 points before the 2014 Giro. Andy Schleck had 526 points before the 2007 Giro. José Rujano had 409 points before the 2005 Giro. Santiago Perez had 478 points before the 2004 Vuelta. Yaroslav Popovych had 601 points before the 2003 Giro.
Cunego was 22 and had done 1 GT, in his third season on a pro team.
Aru was 23 and had done 1 GT, in his second season on a pro team.
Andy Schleck was 21 in his debut GT, in his third season on a pro team.
Rujano was 23 in his debut GT, had barely raced outside South America and was on his third season on a ProConti team.
Popovych was 23 and had done 1 GT, in his second season on a pro team.
Pérez is the outlier, 27 and in his 5th GT, although in fairness he had crashed out of his first two by half distance.
Froome was 26, in his 4th GT, in his fifth pro season and fourth in a higher level team.
For the earlier guys like Aitor González it's a bit more difficult to gauge accurately because of the lack of scores from 1998 back, although I don't think that would change too much in his particular case.
The other thing you could look at is the number of points
that year prior to the GT, obviously bearing in mind when in the season those races are too.
Cunego had 396 points in 2004 prior to the Giro
Aru had 78 points in 2014 prior to the Giro
Schleck had 133 points in 2007 prior to the Giro
Rujano had 273 points in 2005 prior to the Giro (helped a lot by the inflated status of Langkawi)
Pérez had 109 points in 2004 prior to the Vuelta
Froome had 62 points in 2011 prior to the Vuelta
González had 649 points in 2002 prior to the Vuelta