Preface: What I was doing here is by no means optimal or even all that good an idea for actual play, it was more of a thought experiment / theorycrafting to get the most out of the spell Hydraulic Push.
The key focuses were twofold: Boosting the bullrush's CMB as high as feasably obtainable and obtaining Greater Bull Rush (GBR) as early as possible without significantly reducing your CMB in the process. Pure Sorcerer's BAB progression is so low that you wouldn't quality for GBR until 12th level, so dips and prestige classes are likely necessary.
At this point some may argue 'Why get Greater Bull Rush if it says right in Hydraulic Push that "This bull rush does not provoke an attack of opportunity."' For the sake of this thought experiment, we're going to go with the assumption that RAI it meant that performing a bull rush in this manner doesn't cause you to personally provoke AoOs as it would normally otherwise.
Benchmark points I will be using are 1st, 5th, and 9th level. Why these numbers? 1st level to see its base power, 5th because at the time I was discussing this with some friends, this was the level we considered starting at, and 9th because that was the earliest I could manage to obtain GBR.
Things to consider for this build: Hydraulic Push has no saving throw, so effects that affect the save DC of the spell do not increase its power in any way. The Push is based on Caster Level + Highest main casting stat (Int, Wis, Cha), however ultimately you are performing a bull rush, so effects that grant flat + to Bull Rush attempts should still apply. For this build I put most of my focus into Sorcerer, however Druids, Magus, and Wizards can all too learn Hydraulic Push, so perhaps one of them can do it to even greater effect?
~~~~ Current build: ~~~~
Dwarf Empyreal Sorcerer (I wanted Tattooed Emyreal but the Archtypes sadly don't stack. Empyreal's Arcana makes Wisdom our casting stat, instead of Charisma.)
Relentless Dwarftrait grants +2 to Bull Rush (BR)
20 Point Buy after Racial Adjustment: +2 Wis/Con, -2 Cha
13 / 10 / 11 / 13 / 20 / 6
Charisma tanks, and 13 Str /13 Int are necessary as feat requirements. 20 Wisdom gives us +5 to the BR DC of Hydraulic Push (HP) I wish I could manage higher dex or con, but not much wiggle room here.
Trait-traits I took Magical Knack (Sorcerer) and any of the +1 to a single spells CL (Hydraulic Push) traits. I could take two separate +1 CL to a single spell traits, but I need Knack to offset the multiclassing hit I take later on.
1st Level Feat: Spell Focus (Evocation). This does not in any way help power up HP as it affects spell DC's, however its required for Mage Tattoo and Spell Specialization which will both increase its power.
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By the end of character creation we have:
Hydraulic Push: 1d20 + CL 1 + 5 Wis + 2 BR + 1CL Trait = 9. Not great, but it's a start.
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By 5th level, our Wisdom goes up to 21 at 4th. New feats are:
3rd: Spell Specialization (Hydraulic Push) for +2
5th: Mage's Tattoo (Evocation) for +1
Using the recommended gold for a 5th level character (10,500gp), we purchase:
Gauntlets of Skilled Maneuvers (Bullrush) for +2 and a Headband of Inspired Wisdom for +2 to Wis, granting another +1.
At 5th level Hydraulic Push: 1d20 + CL 5 + 6 Wis + 4 BR + 1CL Trait + 1 Tattoo + Specialization 2 = 19.
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By 9th level here is where it gets murky so I'm not sure we're still pushing the max amount. At 7th level we take a single level of Figther to gain all the martial weapon proficiency required for Eldritch Knight at 8th and 9th. Magical Knack offsets the 2 CL loss that Fighter 1/Knight 1 would hit us with, and the BAB from Fight/Knight lets us qualify for GBR at 9th. I couldn't find any way to get GBR sooner than this without significantly reducing the power of Hydraulic Push.
Fighter Bonus Feat 7th level: Power Attack
7th Level: Lingering Spell Metamagic (Goes nicely with HP, couldn't find any other feats to boost HP's power at this time so its a "free" slot essentially. Perhaps Spell Penetration would be more suitable?)
Eldritch Knight Bonus Feat 8th Level: Improved Bull Rush (+2)
9th: Greater Bull Rush (+2, bull rushes provoke AoO from allies.)
At 8th level we also increase our Wisdom by 1 to gain another +1 to Wis.
New Item Purchases are:
Wisdom Headband +4 for +2
Belt of Thunderous Charging +2 BR
Pauldrons of the Bull Allows you to roll all Bullrush attempts twice and take the better result.
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Final 9th level Hydraulic Push:
1d20 + CL 9 + 8 Wis + 10 BR + 1CL Trait + 1 Tattoo + Specialization 2 = 31! and two rolls take better result every time.
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Ultimately you're still a terrible Sorcerer with a bizarre focus, it was just fun to figure out how it could possibly work. I'm sure I made mistakes in both math and finding the best possible choices to do this. Other options I had considered were an Crossblooded Undine Elemental Body [Water] / Aquatic Bloodline seemed promising. At 9th level the Shaitan Bloodline lets you perform bullrushes any time one of your spells damages an enemy which could be worth looking into as well. People have also reccomended to me a Wizard with a staff-like wand of Hydraulic Pushes, which I hadn't considered.
I know this is a huge wall of text but I wanted to show my work, and if anyone can see anything that could improve this, I'm wide open to critique and would super appreciate it. I hope this is the right place too.