Your title suggests one hit, but your description adds
the idea is to not prepare for a day just to make a single hit, but to be able to reliably deal high damage in short instances with just fists alone.
In that case, let me suggest
The Pugilist
Custom Lineage, Darkvision, Skill Expert +1 STR, Stealth (because Surprise), Athletics (expertise because grapple/shove)
14 Str, 14 Con, 13 in Dex, Wis, whatever in Int and Cha (+2 Str)
Fighter 1, Unarmed Fighting (d8 since we aren't wielding any weapons), Perception, Intimidation (your choice), Second Wind
For equipment, two handaxes (for throwing) and Chain mail. When you get some money, switch out the handaxes for javelins (for range). Dump the chain mail when you get Unarmored Defense, as we can't get the bonus Monk attack when wearing armor.
Monk 1 (level 2), for Martial Arts bonus action unarmed attack
Fighter 2-5 (level 3-6), Action Surge, Champion, Crusher feat (+1 STR), Extra Attack
Barbarian 1-3 (7-10), Rage, Reckless Attack, Path of the Beast (extra attack with claw - note, you probably have to use the claw at least once (d6 slashing instead of d8 bludgeoning) and gain one extra claw attack.
Fighter the rest of the way for Extra Extra Attack (F11, class level 15) and feats, Slasher (+1 Dex), ASI CON, Sentinel, Resilient Wisdom, ASI STR, or whatever suits you.
When you consider the attacks are not magical, this becomes less and less effective as more enemies have resistance to non magical attacks. Ideally you would get two common, one hand (each) Eldritch Claw Tattoos. That or dip back into Monk for 5 more levels, but that would add some redundancy, a few features, and delay the extra fighter feats and Extra Extra Attack.
Attacks at level 10, (sustained with Reckless Attack, no Rage)
- Unarmed d8 bludgeoning +STR
- Unarmed d8 bludgeoning +STR (Extra Attack)
- Bonus action (from Martial Arts), Unarmed d8* bludgeoning +STR
* You can substitute your Martial Arts die (d4), but you don't have to :)
DPR ~22.38 (baseline 16.1)
With Action Surge, Reckless Attack and Rage (probably 2x per day)
- Unarmed d8 bludgeoning +STR +Rage
- Unarmed d8 bludgeoning +STR +Rage (Action Surge)
- Unarmed d6 slashing +STR +Rage (claw) (Extra Attack)
- Unarmed d6 slashing +STR +Rage (claw) (Extra Attack, Action Surge)
- Unarmed d6 slashing +STR +Rage (claw) (PoB)
(Bonus action used to Rage)
DPR ~43.88 (baseline 18.77, this looks like a lot, but at 11 baseline goes to 27)
With Reckless Attack and Rage (subsequent to Action Surge)
- Unarmed d8 bludgeoning +STR +Rage
- Unarmed d6 slashing +STR +Rage (claw) (Extra Attack)
- Unarmed d6 slashing +STR +Rage (claw) (PoB)
- Bonus action (from Martial Arts), Unarmed d8 bludgeoning +STR +Rage
DPR ~35.10 (baseline 18.77)
Considerations
You may score at least one crit (47%), especially on Action Surge (65%). If that's a bludgeoning attack, that will benefit your off turn reaction attack from Sentinel (since you can't use Reckless Attack off turn, but Crusher will give you advantage until your next turn on a crit). Crusher also gives you some mobility options, as you can move an enemy with 5' reach and move away without provoking. It also gives you some good options for pushing enemies into hazards. If you crit with slashing damage, your enemy will have disadvantage on its attacks until the start of your next turn. Any hit with slashing damage can reduce the target's speed by 10', once per turn.
This is not a phenomenal damage dealer, but enough to beat the baseline. At least with respect to melee, you cannot be unarmed. This could work well with a city adventure with strict laws or any adventure where you are captured and stripped of your belongings.
The ability to throw weapons will help maintain rage as well as give you some options when enemies are not in melee range. You won't be using any object interactions normally, so drawing and throwing one thrown weapon will be an option. At Fighter 10, you could choose Thrown Weapon Fighting to give you a damage boost as well as be able to throw two weapons using Extra Attack, three at Fighter 11.
This build cannot boost unarmed strike damage with Great Weapon Master or Sharpshooter, so it's going to be behind builds that take advantage of those feats. On the other hand, we get a bonus action attack from Monk, and an extra attack from Path of the Beast - Claw while raging, so that helps balance the missing damage boost, as well as not taking the attack penalty, so you'll hit more often, especially when using Reckless Attack.
This character also has expertise in Athletics, making them very good at grapple/shove or grapple drag, so that will open up a lot of options and make you hard to pin down.
Armor class is a weak point. In order to get the extra attack from Martial Arts, we cannot be wearing armor, so even with Unarmored Defense from two classes, they don't stack, so we just get the best of either. Boost CON and consider boosting DEX.
Sustained damage is good and probably two to three rounds per day, depending on short rest frequency, very good, with a boost to sustained from Rage for the rest of the combat.