Zero Binder Levels
Stupidly, anima mage does not require levels in binder at all. The Bind Vestige and Improved Bind Vestige feats are sufficient to meet the binding prerequisite:
Special: Ability to bind a 2nd-level vestige
That’s all there is to it, and Improved Bind Vestige says this:
Benefit: When you bind a vestige using the Bind Vestige feat, you do so as though you were a 5th-level binder. Thus, you have access to vestiges up to 3rd level, though you still can bind only one at a time and gain only one power from it.
Worse, the sloppy wording of the anima mage's Soul Binding class feature means that if you have no levels in binder, anima mage levels "stack" with your zero levels, so that you make pacts as a binder of the same level as your anima mage level would.
Soul Binding Bonus: At each anima mage level, your soul binding ability improves as if you had also gained a level in the binder class. Your anima mage levels and binder levels stack for the purpose of determining your bonus on binding checks, the effectiveness of your vestige-granted abilities, your ability to bind higher-level vestiges, and the number of vestiges you can bind. You do not, however, gain any other benefit a binder would have gained.
Nothing in there says anything about “existing” binder levels or levels in a binding class you had before taking the prestige class. Compare the very next section, on the anima mage’s spellcasting:
Spellcasting: At each anima mage level, you gain new spells per day and an increase in caster level (and spells known, if applicable) as if you had also gained a level in an arcane spellcasting class to which you belonged before adding the prestige class level.
So, for example, a wizard 3/anima mage 3 casts spells as a sixth-level wizard and binds vestiges as a third-level binder.
It goes without saying that doing this makes the two feats worthless, except for avoiding binder levels.
Effective Character Level: cannot be 1st
You can never take anima mage as your first level character level because prestige class prerequisites must be met the level before you take the class, and you'd never get the spellcasting requirements without class levels anyway.
Achieving the minimum-level entry: ECL 2 (many options 1/Anima Mage 1)
It is possible to enter anima mage at second level, however, as a human with flaws. You need four feats: any metamagic feat, Bind Vestige, Improved Bind Vestige, and Precocious Apprentice from Complete Arcane (page 181, not with the rest of the feats), or some other single-feat early-entry trick for 2nd-level spells.
There are also skill requirements to worry about: 4 ranks each of Intimidate and Knowledge (the planes). Strictly speaking, the level-up rules have you choose skills before feats or gain class features, so you have to be a class that gets both of these as class skills; you cannot rely on a feat to give them to you if you want 4 ranks at 1st level.
For several classes (bards, beguilers, maybe shadowcaster, and arguably warlocks oddly enough), this is all you need, since those classes have Intimidate and Knowledge (the planes) in-class.
For wizards, that means being an enchanter with the Social proficiency variant from Unearthed Arcana. As a variant class, the social proficiency enchanter gets Intimidate in-class natively, not as a separate class feature.
Sorcerers and others: minimum ECL 4 (Sorcerer 3/Anima Mage 1)
Sorcerers can get Intimidate by taking the Battle Sorcerer variant from Unearthed Arcana, but I can find no variant that gives sorcerers Knowledge (the planes) in-class (the Planar Sorcerer substitution levels have it, but the earliest you can take one is Sorcerer 5). So for a sorcerer, the minimum ECL is 4, as the sorcerer needs to take a feat to get Knowledge (the planes) in class but neither has the option of getting such a feat at 1st (already spent all his feats) nor could he choose his skills from 1st level after taking the feat even if he had one, so he has to wait until 3rd level to get another feat.
Several other classes (e.g. dread necromancer, warmage, wu jen) are in a similar situation (lacking one or both of Intimidate and Knowledge (the planes) in-class, and have the same minimum. Non-enchanter wizards are almost in this situation, but the Fighter Bonus Feat variant allows the wizard another 1st-level feat, which could get Intimidate in-class and allow entry as Wizard 2/Anima Mage 1 (ECL 3).
I strongly recommend all DMs ban this, however
With a single binder level and the Improved Binding feat, you qualify for anima mage and actually have the Soul Binding class feature to progress. This is far more balanced and appropriate, so I strongly recommend that DMs require that single-level dip.
Preventing Improved Binding from working, and requiring three levels of binder, is going too far. That makes anima mage a huge self-nerf that doesn’t seem appropriate.
Banning Precocious Apprentice and other early-entry spellcasting tricks is also strongly advised.
So the result is prepared-caster 3/Binder 1/Anima Mage 1 or spontaneous-caster 4/Binder 1/Anima Mage 1. So I suggest that you consider ECL 5 the first level you could take as anima mage as a sorcerer.