What is the earliest a bloodrager qualities for arcane strike with only bloodrager levels to qualify for it?
I think it's 4th but maybe it's first unlikely but i still have to ask.
You would need to be able to cast any arcane spell. Per the FAQ you can qualify using spell like abilities. If your race or your Bloodline granted a spell like ability that is an arcane spell then you qualify.
Otherwise, 4th level when he gets his first spell.
If they have an arcane spell-like ability at first level(like gnomes do), then yes, you can pick it up at 1st level. Otherwise you need to be 4th level.
Strangely, unlike Paladins or Rangers, who specify they're caster level is their Paladin/Ranger level -3, Bloodragers cast at caster level 4 as soon as they get spells.