As a preface, this guide is intended for people who want to minimise the time/skill investment required to get a 32 heat run. This strategy got me the statue before I even knew summons were a thing or had 10 wins and saw the true ending. I do not believe it requires much skill to win the game playing like this, and my getting this run so early is the proof of that.
The weapon of choice is a maxed aspect of demeter, but a maxed aspect of gilgamesh and/or whatever the crit sword aspect's called will both work fine as well for the purposes of this build. I'll elaborate further on why later, it's more important to talk about the pact of punishment first...
Pact of Punishment
I think the most important concept to grasp as a new player is that, as someone without the hours invested to build experience and skill, it's unrealistic to be able to dodge every attack and it's also very time-costly and requires constant high-intensity thinking to be cognisant of everything that's going on in each room. If you're just looking to get the statues with as little time investment as possible you will have to accept that you'll be getting hit a lot, and as a result, we want our pact to take that in to account. This guide only gives 23 concrete heat points, so there's flexibility with the pact you'll end up with but to go over each condition:
Hard labor: when you're getting hit a lot, enemies dealing more damage is a problem, so we want this to be as low as we can get away with.
Lasting consequences: this is just an inverted version of hard labor in a way, so the same applies.
Convenience fee max (2): just think of shops as a heal stop 90% of the time and this is essentially 2 free points. It's rare that the alternative option to a shop isn't something that's also valuable, so you're often not losing out on much by maxing this.
Jury summons: points in this are much less of a time investment or danger of damage than is immediately apparent due to the high aoe potential of zagreus in general, but it's still not ideal to take more points than you need to.
Extreme measures 3 (6): I did not have extreme measures 4 unlocked when I completed my run, but if you feel comfortable with fighting extreme hades then your pact options will be much more flexible due to the high heat bonus. I do not personally believe that the increased difficulty is worth 4 heat for the purposes of trying to unlock the statue as fast as possible (the theme of this writeup), but with enough playtime and experience with the fight it'll eventually become an efficient choice for reaching 32 heat for any player.
Calisthenics program: absolutely not worth the point investment, bosses are the biggest threat of death in the run and have naturally high health pools, and it's also time inefficient. If you're desperate for points, 1 at the absolute most.
Benefits package: among the better options for the last 9 points of heat. If you're taking one point in this you should probably be taking the second, having tried both I can't say the difference between one and two boons on armored enemies is all that noticeable compared to the difference between 0 and 1?
Middle management max (2): this is generally two free points. The only mini-boss that becomes particularly scary because of this is the medusa head + thwomp and there's a good chance you'll get the barge or just bypass them altogether instead.
Underworld customs max (2): you don't need many boons to deal sufficient damage with the listed aspects so unless you get unlucky this is another 2 free points.
Forced overtime max (6): very point efficient and many of the base enemies in game don't become any harder to deal with. One again, we're expecting to get hit a lot, for the first few attempts it'll feel strange if you aren't used to it but it's very easy to adapt to for the point value imo.
Heightened security: the only reason you'd ever take this is if you ensured you got the athena boon to counter it, and even then it wouldn't be worth 1 point honestly, it's probably the least efficient condition in the game for how much danger it adds.
Routine inspection: taking one point of this is generally a good idea but isn't 100% required, any more than one point isn't worth it unless you're going for more than 32 heat.
Damage control max (2): is not a concern for the playstyle we'll be aiming for, and kinda always worth the 2 point investment at this heat.
Approval process: if you want to brute force it by start scumming then 2 points in this is probably an option, but that's lame. 1 Point is fine, it'll make the game more variant but our boon options are open and not difficult to find.
Tight deadline 2 (3): the playstyle we'll be aiming for is very much based on keeping our damage as high as possible even at the cost of taking hits, so unless you feel it'll be too stressful for you, I'd suggest maxing this. You'll only really be at risk of timing out in tartarus if you get a string of bad rooms, otherwise I'd honestly expect that it's unlikely it'll take more than 20 minutes to finish the run.
For the remaining 9 heat, it'll always depend on your skillset. Jury summons 1 (+1), benefits package max (+5) and tight deadline max (+3) is what I'd personally go with now, but my first 32 heat completion used approval process 1 and routine inspection 1 (+4) instead of benefits package, I forget what the last point was but 4 of the 5 options are fine. There are a lot of ways to get the remaining 9 heat, especially if you're comfortable with extreme measures max, so just figure out what's best for you to finish off the pact!
Boons + Summary
Remember that our goal is to output as much damage as possible in as little time as possible to avoid having to think about dodging as little as possible. The three weapon aspects available are all choices because of their synergy with the single required boon:
Tidal dash: this boon does absolutely everything in one slot, and you should be spamming the dash button for the entire run to get the most use of it, more or less. Because our weapon already requires us to get on top of the enemy we'll always be benefiting from the damage (which is extremely high), it clears projectiles and also pushes enemies away so it provides you with a lot of safety, and it enables a playstyle where you herd the enemies together and as a result is incredibly time efficient. I don't think I've ever regretted taking this over athena dash regardless of the weapon I was using, honestly, once you get a feel for the pulse delay it protects you from projectiles more than sufficiently. Passion dash is the only other option I'd consider but the loss of damage is most likely not worth it, we can get the debuff in other slots.
Past tidal dash it's a bit more dependent on which of the three listed choices you take, but here are some boons that are good for all of them:
Crashing wave (poseidon): enemies start to melt like butter if you make good use of this boon. Not useful against bosses, but makes the rest of the game a much smoother ride, it's always worth taking in the first three stratums.
Wave pounding (poseidon): tidal dash dps is already high, making it higher against bosses will always be a good thing.
Greatest reflexes (hermes): this in combined with tidal dash alone is enough damage to get through the game. Non-bosses will probably start to feel absolutely trivial if you get this boon and it's rare or better. (This is also why the aspect of gilgamesh is a very appealing option)
Hyper sprint (hermes): the increased mobility is really nice for boss fights, the 100% uptime on sturdy is absolutely amazing when you're expecting to get hit a lot.
Heartbreak strike/flourish (aphrodite): if you manage to get weak + sturdy (through hammer for fists or hyper sprint) + tidal dash you'll start to notice just how little skill it takes to win, even on 32 heat. Both also happen to have high damage percentages which is a nice bonus!
Nourished soul (demeter): healing more means your mistakes are less costly. It's that simple really
Strong drink (dionysus) a better version of nourished soul.
Hammers (fists): don't take rending claws or rolling knuckle. You won't be using special much if ever on gilgamesh so quake cutter is not useful, and draining cutter, while nice, is not ideal to set up when you're focusing on dealing as much damage as possible. Flying cutter is good but is honestly really annoying to use given that you're dashing around constantly and you have to avoid dash-uppering to make use of it. Every other hammer for fist is solid; explosive upper is generally the best option to take whenever it's available!
Hammers (sword): cursed slash is a bad idea generally since dash-strike doesn't proc it, but with weak + sturdy I'm sure it could end up being really facerolly. Cruel thrust is rarely going to proc for you and special boons aren't super useful since you're only using it for the crit chance but it's not like it's hurting you to take them? In general just about anything works here, but double edge, piercing wave and breaking slash are doing the most for us.
There are many other good boons for this build, as well, but the point to begin with is that we want to simplify the process of getting a win as much as possible. Focusing on poseidon and aphrodite through keepsakes makes getting the run online very simple and consistent, but feel free to use acorn or spearpoint or even plume or pom blossom for the whole run if you want, it's up to you.
Just be cognisant that this is a playstyle of blinding aggression: you want to be dashing at the enemy constantly without much regard for what they're doing. Once you're on top of them, just dashing back and forth on the spot and attack spamming is extremely effective at making most enemies unable to do anything to you.
(If you happen to have a maxed bouldy pet I'd assume that the pocket heals would make winning significantly easier, as well, but I haven't unlocked him yet so I can't say for sure.)