Falling Damage is a good way that you can control fatal damage.
- Dice are involved, and may thwart your designs
- You don't control the environment, the DM does.
I've fallen and I can't get up.
You have to set yourself up to fall at least 40 feet if you are a 1st level character, but I'd recommend falling at least 50 feet.
Why? Your objective is that the character is subjected to 'Instant Death' upon impact.
1d6 of damage per 10' feet of falling. Average 3.5
50' gives you 17.5 damage, on average.
60' gives you 21 damage, on average.
Dropping to 0 Hit Points(Basic Rules, p. 75)
When you drop to 0 hit points, you either die outright or fall
unconscious, as explained in the following sections.
Massive damage can kill you instantly. When damage reduces you to 0
hit points and there is damage remaining, you die if the remaining
damage equals or exceeds your hit point maximum. For example, a
cleric with a maximum of 12 hit points currently has 6 hit points. If
she takes 18 damage from an attack, she is reduced to 0 hit points,
but 12 damage remains. Because the remaining damage equals her hit point maximum, the cleric dies.
If you choose a 1d6 HD character (Sorcerer or Wizard) you are most likely to do more than your maximum HP of extra damage and be killed outright; your character is dead.
But the Dice May Betray You
From 50' up, you have a 99% chance to simply drop to 0 HP and be ... mostly dead. (Take at least 8 damage, which is 1d6 plus an expected 2 HP for a Constitution bonus). The trouble for your plan is with the death saving throws as you lie there if you take less than double maximum damage.
Death Saving Throws (Basic Rules p. 76)
Whenever you start your turn with 0 hit points ... make a
special saving throw, called a death saving throw ... Roll a d20. If
the roll is 10 or higher, you succeed. Otherwise, you fail.
On your third success, you become stable (see below).
On your third failure, you die.
The successes and failures don’t need to be consecutive; keep track of both until you collect three of a kind. The number of both is reset to zero when you
regain any hit points or become stable.
Your party may thwart your plan buy using healing, or a spell, or an ability to make you stable. That is why taking twice your maximum damage is so important. They can't aid you if you suffer instant death. Even so, fall away from, not toward, the party to make their helping you less likely.
But those traitorous dice can foil your plot on a single roll if you do less than twice maximum, with a natural 20 on any death saving throw.
If you roll a 20 on the d20, you regain 1 hit point.
The difference between 1 HP and 0 is a step function. 1 HP, alive. 0 HP, dead or dying.
Stack the odds in your favor; fall from as high as you can.
This anydice roll of 5d6 demonstrates how you are unlikely to survive a 50' fall. The chance that you'll do at least 14 damage in 85% (representing a 1 HP constitution bonus) and at least 16 70% (representing a 2 HP constitution bonus).
Precisely how to do that in a given encounter is up to your taking advantage of the opportunity, and making an attempt to do something that results in your falling at least 50' ... the higher the better.
Play with the anydice function, to increase the 5d6 to higher values to 6d6 or 7d6 to see how close you can get to a fall with a very high 90's percentage chance of double your damage.
The game won't do this for you; carpe diem!
Your challenge is to find something very high, and have your character fall off of it in a way that does not look obvious. (That is up to your role playing skill). Part of your requirement is that it not look like a suicide, so you have to establish early on that your character likes to climb things, whether or not that character is any good at it. You'll need to be subtle about this or you'll tip your hand on the "suicide by gravity" scheme.
And I won't forget to put roses on your grave ...
Final Caveat: Rule Zero
The DM may, when you fall, fudge the damage role. No rule in the book can (technically) overwrite Rule Zero.
Also, the DM, who looks to be setting you all up with pre-generated characters, may simply offer you another pre-generated character to replace the dead one so that you can keep on playing. There's nothing in the above answer, nor in the game engine, nor in the rules, that can in a foolproof way solve that social (and perhaps for you, awkward) scenario. If you arrive at that point, Zeiss Ikon's answer might look really attractive.