so provided your second and third levels are fighter, and you don't lose any BAB until 6th, yeah you can manage.
Fighter Bonus Feats are Martial Study and Martial Stance (at 2 and 3 respectively), standard lvl 3 feat is shadow blade, and gloom razor at 6.

Alas AFAIK there is no single class level that boosts your BAB by 2, or feat that does so by 1.