The easy part: skills and spells…
A typical wizard or sorcerer doesn't have as class skills the skills Bluff, Diplomacy, Intimidate, and Sense Motive. This usually delays the creature's entry into the prestige class mindbender (Complete Arcane 54-6) to at least character level 5 because of the maximum ranks that can be put into cross-class skills.
The easiest way for a creature to meet this requirement early is to gain the class feature social proficiency (Unearthed Arcana 61) the creature must be a specialist wizard—an enchanter—, and the creature "does not gain bonus feats for advancing as a wizard." Ask the DM if this means the creature also doesn't gain at level 1—like a typical wizard does—the bonus feat Scribe Scroll (Player's Handbook 99-100). This DM thinks the creature would still gain the bonus feat Scribe Scroll based on the way the ability's written, but confirm with your DM that it's legit that the creature'll essentially be getting something for nothing.
Among other benefits, the special ability social proficiency has the creature "[a]dd the following skills to [its] list of [specialist] wizard class skills: Bluff, Diplomacy, Gather Information, Intimidate, and Sense Motive." Yes, the skill Gather Information is there, too, because why not, right?
Anyway, with the special ability social proficiency the creature—if a human enchanter with at least Intelligence 12—can meet the skill rank requirements of the prestige class mindbender at level 1. Note that the Unearthed Arcana section in which it appears is called Specialist Wizard Variants, and the special ability is supposed to be used—along with the others for enchanters and for other specialist wizards—by the DM to customize the campaign setting and not really as artifacts available generally. I can't imagine most DM's having a problem with this, but aiming for early entry shenanigans means even the smallest flaw might ruin the plan.
Alternatively, the feats Academy Graduate (Savage Tide Player’s Guide 8) and Flexible Mind (Dragon #326 80) combined can make all the necessary skills always class skills (plus another skill the creature picks—likely the skill Use Magic Device). This also allows meeting the prestige class's skill requirements at level 1 (or at level 2 under some readings of the feat Flexible Mind). (The feat Able Learner (Races of Destiny 150) isn't useful here; it's benefit says, "The maximum number of ranks you can purchase in a cross-class skill remains the same.")
…And the hard part: arcane caster level 5th
While there are undoubtedly other ways to meet the mindbender requirement Arcane caster level 5th, no easy method of early entry withstands serious scrutiny given the question's binds. Folks have been hunting through official texts for years in attempts to raise artificially a creature's caster level so as to meet prestige class requirements early, from the now defunct Wizards of the Coast's forums archived here, to EN World's forums here, to RPG Net's forums here, and repeatedly—over and over again, even—on the Giant in the Playground forums, searched for convenience here.
The constant is the ioun stone (orange prism) (Dungeon Master's Guide 260-1) (30,000 gp; 0 lbs.). Everything else—when subjected to the strictest reading—fails the question's test of, essentially, needing the arcane caster level increase to persist all the time forever.1
For example, the ring of arcane might (Magic Item Compendium 121-2) (20,000 gp; 0 lbs.)—the ioun stone (orange prism)'s closest competitor— specifies that its +1 bonus to the wearer's caster level applies only "for the purpose of spell penetration checks, caster level checks, and all level-based variables of any arcane spells [the wearer] cast[s]," that last part being the sticking point. So, rather than applying in general, using a really strict reading the caster level bonus of the ring applies only when actually casting spells and not when, for example, sleeping, making it situational therefore inapplicable. (Note that this DM and player doesn't encourage that the ring be read this way generally; it's read this way here deliberately to demonstrate the question's restrictions.)
Feats that increase caster level are usually even more specific in that they'll typically increase the feat's possessor's caster level for spells of a specific school of magic, spells possessing a a specific descriptor, spells cast while in a certain place or during a certain time, or even spells of a specific name. None of these feats allow the creature to meet that the prestige class requirement more quickly given the question's binds.
Entering the prestige class mindbender any sooner than as a level 4 arcane caster by acquiring early—nearly 25,000 gp early, in fact—the ioun stone (orange prism), is, I think, given those binds, impossible.
What remains then is the question's last resort: meeting the arcane caster level 5th requirement of the prestige class mindbender through temporary means. The easiest and earliest way is by employing the standard strand of prayer beads (DMG 267-8) (25,800 gp; 0 lbs.)… perhaps absent the bead of healing and the bead of smiting. The creature may have to borrow a standard strand from a church if the creature can't get for free a standard strand with only the bead of karma.2
To use this method, the creature gets within a hairsbreadth of the XP required for level 2, cautiously acquires the standard strand, carefully constructs a CR ½ booby trap (Dungeon Master's Guide II 41) (50 gp or less; trap)—I recommend the alarm booby trap—, and succeeds on a Use Magic Device skill check to emulate the class feature spells of a level 1 cleric (DC 21), convincing the the bead of karma to activate. For 10 min. the "[w]earer casts his spells at +4 caster level," the bead not caring if the spells are arcane or divine. Then, before 10 min. have passed, the creature encounters the booby trap, earns its 150 XP, and cackles maniacally as it takes its first step along the path of the prestige class mindbender.
Of course, gaming XP gain in such a fashion is, I think, generally frowned upon, and the DM must still be convinced that the bead of karma's effect is sufficient to count as increasing the creature's arcane caster level from 1st—because the creature's still an enchanter—to 5th for this purpose, but if the perhaps-too-open-minded DM's been convinced to go this far already, convincing him of that, too, should be fairly easy.
The other, even shadier way: play a race with a spell-like ability
The prestige class mindbender's actual requirement says, "Spells or Spell-Like Abilities: Arcane caster level 5th." Thus a creature with a spell-like ability that can be employed as a level 5 wizard may be able to meet this class's requirement. For example, a duergar (Monster Manual 91, 92) can use as spell-like abilities 1/day each effects like enlarge person and invisibility with a caster level of twice its character level (min. 3). By level 3 (or 4 with its Level Adjustment +1), it sort of meets the mindbender requirement. I say sort of because the DM must agree that such a creature's effective arcane caster level for its spell-like abilities is 5th instead of just its caster level for its spell-like abilities being 5th. This will likely be difficult: this DM supposes that the inclusion in the mindbender requirements of the charm invocation means the class's authors wanted to open up the class more easily to warlocks—that also appear in Complete Arcane (5-8) and that actually have an arcane spellaster level for their spell-like abilities—rather than opening the class even wider to, for example, bald, joyless gray dwarves.
1 The effects of multiple ioun stones (orange prism) don't stack according to the FAQ (62). Make of that what you will.
2 The Dungeon Master's Guide (2003) says to reduce the price of a standard strand of prayer beads by 9,000 gp if it's missing the bead of healing and by another 16,800 gp if it's missing the bead of smiting, hence a net cost of 0 gp for a standard strand with only a bead of karma. The Dungeon Master's Guide (2012) stealth erratas the price of the standard strand of prayer beads to 45,800 gp, so that a standard strand that has remaining only the bead of karma has a price of 20,000 gp.